Two flocks of birds are $210$ miles apart and heading directly toward each other. One flock is flying at a rate of $25$ miles per hour. In comparison, the other flock is flying at a rate of $37$ 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

View step-by-step help

Home

Math Problems

Algebra 1

Rate of travel: word problems

Full solution

Q. Two flocks of birds are

210

miles apart and heading directly toward each other. One flock is flying at a rate of

25

miles per hour. In comparison, the other flock is flying at a rate of

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

Rephrase the Problem: First, let's rephrase the ＂How long will it take for two flocks of birds flying towards each other from $210$ miles apart to meet if one flies at $25$ mph and the other at $37$ mph?＂
Calculate Combined Speed: We need to find the combined speed of both flocks of birds. The first flock is flying at $25$ miles per hour, and the second flock is flying at $37$ miles per hour. To find the combined speed, we add these two speeds together. $\newline$ Combined speed $=$ Speed of first flock $+$ Speed of second flock $\newline$ Combined speed $= 25 \, \text{mph} + 37 \, \text{mph}$ $\newline$ Combined speed $= 62 \, \text{mph}$
Calculate Time to Meet: Now, we will calculate the time it takes for the two flocks to meet. We know the distance between them is $210$ miles, and we have just calculated their combined speed to be $62$ miles per hour. The time taken to meet can be found by dividing the distance by the combined speed. $\newline$ Time $=$ Distance $/$ Combined speed $\newline$ Time $=$ $210$ miles $/$ $62$ miles per hour
Divide to Find Time: Performing the division to find the time: $\newline$ Time $\approx 3.3871$ hours $\newline$ However, we need to round the answer to the nearest minute. First, let's separate the hours from the minutes.
Separate Hours and Minutes: The number of whole hours is $3$ . To find the remaining minutes, we take the decimal part and multiply it by $60$ (since there are $60$ minutes in an hour). $\newline$ Minutes = $0.3871$ hours $\times 60$ minutes/hour $\newline$ Minutes $\approx 23.226$ minutes
Round to Nearest Minute: We round the minutes to the nearest whole number: $\newline$ Minutes $\approx 23$ minutes $\newline$ So, the two flocks will meet in approximately $3$ hours and $23$ minutes.