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Math Problems
Algebra 1
Rate of travel: word problems
Two flocks of birds are
210
210
210
miles apart and heading directly toward each other. One flock is flying at a rate of
25
25
25
miles per hour. In comparison, the other flock is flying at a rate of
37
37
37
miles per hour. In how much time will the two flocks meet?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
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Darnell and Roxanne just finished a picnic at the park and are about to ride their bikes home. Darnell goes
6
6
6
miles per hour, and Roxanne goes
7
7
7
miles per hour in precisely the opposite direction. In how long will they be
10
10
10
miles apart?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
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A large ice floe is floating toward a polar bear
7
7
7
kilometers away at a speed of
2
2
2
kilometers per hour. At the same time, the polar bear is swimming toward the ice floe at
5
5
5
kilometers per hour. How long will it be before the polar bear reaches the ice floe? If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
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A rescue boat just picked up some sailors in a lifeboat. Now the rescue boat is heading north at
14
14
14
miles per hour. The lifeboat, which they abandoned, is drifting south at a speed of
3
3
3
miles per hour. How long will it be before the rescued sailors are
57
57
57
miles from their lifeboat?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
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Helen and Reid are walking to their classes at Cedarburg College. Helen comes from her dorm room, walking at a speed of
4
4
4
miles per hour down a straight path. Reid comes from the gymnasium on the other end of campus, moving up the same path at
3
3
3
miles per hour. If they start out
3
3
3
miles apart, how long will it be before they meet?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
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Helen and Elizabeth just met up in Springdale for the afternoon, and now it is time for them to get in their cars and head home. Helen heads due east at
95
95
95
kilometers per hour, and Elizabeth heads due west at
89
89
89
kilometers per hour. How long will it be until they are
77
77
77
kilometers apart?
\newline
If necessary, round your answer to the nearest minute.
\newline
_
_
_
\_\_\_
___
hours and
_
_
_
\_\_\_
___
minutes
\newline
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Two friends, Zeke and Marshall, are going to depart from their houses and ride their bikes toward each other until they meet, and then have a picnic. Zeke can bike
15
kilometers per hour
15 \, \text{kilometers per hour}
15
kilometers per hour
, while Marshall can bike
17
kilometers per hour
17 \, \text{kilometers per hour}
17
kilometers per hour
. If their houses are connected by a straight road that is
8
kilometers
8 \, \text{kilometers}
8
kilometers
long, in how long will the two meet? If necessary, round your answer to the nearest minute.
\newline
_
_
_
_
\_\_\_\_
____
hours and
_
_
_
_
\_\_\_\_
____
minutes
\newline
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Two freight trains leave the station in Allenville at the same time. The first train is headed due south at a speed of
43
43
43
kilometers per hour. In comparison, the second train is going due north at
64
64
64
kilometers per hour. In how long will the trains be
450
450
450
kilometers apart?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
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Two buses are scheduled to arrive at the Middletown Bus Terminal at the same time. One bus is south of the terminal, driving north at
26
26
26
miles per hour. At the same time, another bus is north of the terminal and is driving south at
59
59
59
miles per hour. They are currently
70
70
70
miles apart. How long will it be before the buses arrive at the terminal?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
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Barbara is kayaking on a river in Clinton County, moving down the river at a speed of
8
8
8
miles per hour. Meanwhile, Levi is on a jet ski
5
5
5
miles away, moving up the river at
27
27
27
miles per hour. How long will it be before the two meet?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
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Zane and Camilla are coworkers who live in different cities. They both left the office at the same time today. Camilla drove directly east toward Oxford at a speed of
37
37
37
miles per hour. Zane took the bus directly west toward Westminster, traveling
32
32
32
miles per hour. In how long were the two of them
44
44
44
miles apart?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
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An iceberg and a ship separated by
98
98
98
miles are moving directly toward each other. The iceberg is floating at
1
1
1
mile per hour, whereas the ship is traveling at
12
12
12
miles per hour. Assuming that neither changes course, how long will it be before the two collide?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
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Brett took the train due south from the airport, heading to the end of the line. At the same time, Maddie also left home and started driving due north to the end of the line, where she would pick Brett up. Brett's train traveled
66
66
66
kilometers per hour, and Maddie drove
82
82
82
kilometers per hour. They started out
44
44
44
kilometers apart and arrived at the station at the same time. How long did it take them to meet?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
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Mrs. Richmond's class is on a ferry that is traveling
41
41
41
kilometers per hour. The students notice that they are passing right by a fishing boat that is traveling in exactly the opposite direction at
89
89
89
kilometers per hour. How long will it be before the two vessels are
6
6
6
kilometers apart?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
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Mrs. Brady's class takes a ferry east across a lake at
24
24
24
miles per hour. At the same time, a fishing boat leaves from the opposite side of the lake, traveling west at
52
52
52
miles per hour. The two vessels started out
1
1
1
mile apart and are now traveling directly toward each other. How long will it be before they pass by each other?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
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A twig floats downstream at a rate of
4
4
4
kilometers per hour. At the same time,
2
2
2
kilometers downstream, a trout begins swimming upstream, moving toward the twig at
16
16
16
kilometers per hour. In how much time will the fish swim by the twig?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
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Two freight trains leave the station in Lexington at the same time. The first train is headed due south at a speed of
22
22
22
miles per hour. In comparison, the second train is going due north at
35
35
35
miles per hour. In how long will the trains be
380
380
380
miles apart?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
Get tutor help
Hakim and Frank just finished a picnic at the park and are about to ride their bikes home. Hakim goes
14
14
14
miles per hour, and Frank goes
11
11
11
miles per hour in precisely the opposite direction. In how long will they be
6
6
6
miles apart? If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
Get tutor help
A large ice floe is floating at a speed of
4
4
4
kilometers per hour. A polar bear leaves the floe and swims in the opposite direction at
7
7
7
kilometers per hour. How long will it be before the polar bear is
1
1
1
kilometer away from the floe? If necessary, round your answer to the nearest minute.
\newline
_
_
_
_
\_\_\_\_
____
hours and
_
_
_
_
\_\_\_\_
____
minutes
Get tutor help
A train travels at a speed of
60
km/h
60\,\text{km/h}
60
km/h
, while a car travels at a speed of
80
km/h
80\,\text{km/h}
80
km/h
. How far will the car have traveled when it catches up to the train if they start from the same point and travel in the same direction?
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A car travels at a speed of
60
km/h
60\,\text{km/h}
60
km/h
, while a bicycle travels at a speed of
20
km/h
20\,\text{km/h}
20
km/h
. If they both start at the same time and travel in the same direction, how long will it take for the car to be
30
kilometers
30\,\text{kilometers}
30
kilometers
ahead of the bicycle?
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A bicycle is travelling at
12
12
12
miles per hour. How many feet will it cover in
45
45
45
seconds?
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word problems.
\newline
f you are driving at a constant rate of
108
108
108
kilometers per hour. low long will it take you to travel
270
270
270
kilometers?
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Given that events A and B are independent with
P
(
A
)
=
0.9
P(A)=0.9
P
(
A
)
=
0.9
and
P
(
B
)
=
0.3
P(B)=0.3
P
(
B
)
=
0.3
, determine the value of
P
(
A
∣
B
)
P(A \mid B)
P
(
A
∣
B
)
, rounding to the nearest thousandth, if necessary.
\newline
Answer:
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Given that events A and B are independent with
P
(
A
)
=
0.56
P(A)=0.56
P
(
A
)
=
0.56
and
P
(
B
)
=
0.35
P(B)=0.35
P
(
B
)
=
0.35
, determine the value of
P
(
A
∣
B
)
P(A \mid B)
P
(
A
∣
B
)
, rounding to the nearest thousandth, if necessary.
\newline
Answer:
Get tutor help
4
4
4
. Rupert has a collection of Blu-ray discs he wants to store in a cubical box with edges of length
10
10
10
inches. If each Blu-ray has dimensions of
5
5
5
inches by
5
5
5
inches by
0.25
i
n
c
h
0.25 \mathrm{inch}
0.25
inch
, what is the maximum number of discs that can be fit into the box?
\newline
A)
60
60
60
\newline
B)
80
80
80
\newline
C)
160
160
160
\newline
D)
200
200
200
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A big cruise ship dropped anchor off the Caribbean island of Antigua. The heavy anchor dropped into the water at a rate of
2.5
meters per second
2.5\,\text{meters per second}
2.5
meters per second
. After
45
seconds
45\,\text{seconds}
45
seconds
, the anchor was
40
meters
40\,\text{meters}
40
meters
below the water's surface.
\newline
From what height
above the water’s surface
\text{above the water's surface}
above the water’s surface
was the anchor released?
\newline
□
\square
□
meters
\text{meters}
meters
\newline
How long did it take the anchor to reach the water's surface?
\newline
□
\square
□
seconds
\text{seconds}
seconds
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Two people are at an elevator. At the same time one person starts to walk away from the elevator at a rate of
2
ft/sec
2\,\text{ft/sec}
2
ft/sec
and the other person starts going up in the elevator at a rate of
7
ft/sec
7\,\text{ft/sec}
7
ft/sec
. What rate is the distance between the two people changing
15
15
15
seconds later?
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A
l
l
l
-meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at
v
v
v
meters per minute. At a certain instant, the bottom of the ladder is
b
b
b
meters from the wall. What is the rate of change of the area formed by the ladder at that instant (in square meters per minute)?
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The top of a
25
25
25
foot ladder is sliding down a vertical wall at a constant rate of
4
4
4
feet per minute. When the top of the ladder is
15
15
15
feet off the ground, what is the rate of change of the distance between the bottom of the ladder and the wall?
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A controversial story comes out in the school newspaper. The number of students who have not heard about the story decreases at a rate that is proportional at any time to the number of students who have not heard the story at that time.
\newline
There were
900
900
900
students who had not heard the story initially, and the number of students is divided by
3
3
3
every
4
4
4
days.
\newline
How many students have not heard the story after
7
7
7
days?
\newline
Round to the nearest student.
\newline
□
\square
□
students
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George is driving at an average speed of
70
70
70
miles per hour. At this rate, how long, in minutes, will it take him to complete a
400
400
400
-mile road trip?
\newline
(Round your answer to the nearest minute.)
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Standard movie projectors project
24
24
24
still images, known as frames, each second. If a certain movie uses the standard frame rate and has exactly
129
129
129
,
600
600
600
total frames, then, to the nearest whole minute, how long is the movie?
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A wildfire is spreading toward a ranger station at a rate of
6
6
6
miles per hour. If the ranger station is
5
5
5
miles away from the wildfire, how many minutes will it take for the wildfire to reach the ranger station?
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An airplane begins its descent to land from a height of
35
35
35
,
000
000
000
feet above sea level. The airplane's height changes by about
−
4000
-4000
−
4000
feet every
3
3
3
minutes. Rounded to the nearest minute, in approximately how many minutes will the plane land? Assume that the airport runway is at sea level.
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A whale is swimming due north at a speed of
30
30
30
miles per hour. Just
5
5
5
miles away, a whale-watching tour boat is traveling south, directly toward the whale, at a speed of
46
46
46
miles per hour. How long will it be before they meet? If necessary, round your answer to the nearest minute.
_
_
_
_
\_\_\_\_
____
hours and
_
_
_
_
\_\_\_\_
____
minutes
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