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 $15 \, \text{kilometers per hour}$ , while Marshall can bike $17 \, \text{kilometers per hour}$ . If their houses are connected by a straight road that is $8 \, \text{kilometers}$ long, in how long will the two meet? If necessary, round your answer to the nearest minute. $\newline$ $\_\_\_\_$ hours and $\_\_\_\_$ minutes $\newline$

View step-by-step help

Home

Math Problems

Algebra 1

Rate of travel: word problems

Full solution

Q. 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 \, \text{kilometers per hour}

, while Marshall can bike

17 \, \text{kilometers per hour}

. If their houses are connected by a straight road that is

8 \, \text{kilometers}

long, in how long will the two meet? If necessary, round your answer to the nearest minute.

\newline

\_\_\_\_

hours and

\_\_\_\_

minutes

\newline

Find Combined Speed: We need to find the combined speed of Zeke and Marshall when they bike towards each other. $\newline$ Speed of Zeke: $15$ kilometers per hour $\newline$ Speed of Marshall: $17$ kilometers per hour $\newline$ Combined speed = Speed of Zeke + Speed of Marshall $\newline$ Combined speed = $15 + 17 = 32$ kilometers per hour
Calculate Meeting Time: Now, we need to calculate the time it will take for them to meet. $\newline$ Distance between their houses: $8$ kilometers $\newline$ Combined speed: $32$ kilometers per hour $\newline$ Time $=$ Distance $/$ Speed $\newline$ Time $=$ $8$ $/$ $32$ $\newline$ Time $=$ $0.25$ hours
Convert Time to Minutes: We need to convert the time from hours to minutes. $\newline$ Time in hours: $0.25$ hours $\newline$ Minutes in an hour: $60$ $\newline$ Time in minutes = Time in hours $\times$ Minutes in an hour $\newline$ Time in minutes = $0.25 \times 60$ $\newline$ Time in minutes = $15$ minutes
Final Meeting Time: Since $0.25$ hours is less than one hour, we have $0$ hours and $15$ minutes as the time it will take for Zeke and Marshall to meet.