This question is for College algebra

Question

A cyclist traveled at a rate of 24 mi/hr to visit a nearby town. The cyclist averaged 18mi/hr on the return trip. If the round trip took 4.9 hours, what is the distance to the nearby town?

Answer 1

The distance in each direction is the same.

So the distance on the way there using the rate * time = distance formula is

the rate of 24mph and the time of t

so 24 * t = distance there

on the way back the rate is 18mph and the amount of time it took to come back is 4.9 hrs minus the amount of time it took to get there which is t

so 18(4.9 - t) is the distance back

Since the distances are the same

24 * t = 18(4.9 - t)
24t = 88.2 - 18t
42t = 88.2
t = 2.1

so the time to get there is 2.1 hours

2.1 hours * 24 = 50.4

the time to get back = 4.9 - 2.1 = 2.8 hours

2.8 hours * 18 mph = 50.4

The distance to the town is 50.4 miles