Question

Some kids went on a bike ride. The ride was six hours long and the kids traveled 54 miles. For part of the ride they biked at a speed of 7 miles per hour and for part of the ride they biked at a speed of 11 miles per hour. For how long did they bike at the first speed and for how long at the other speed?

Answer 1

3 hours at each speed

Explanation:

Let t represent the time spent biking at 11 mph. Then 6-t is the time spent biking at 7 mph. The total distance traveled is ...

distance = speed × time

54 = 11t +7(6-t)

54 = 4t +42 . . . . . eliminate parentheses, collect terms

12 = 4t . . . . . . . . . .subtract 42

3 = t . . . . . . . . . . . .divide by 4. Hours at 11 mph.

6-t = 6-3 = 3 . . . . hours at 7 mph

The kids biked at 7 mph for 3 hours and 11 mph for 3 hours.