Expert: Socrates - 3/13/2006

Question
A cyclist traveled at a rate of 24 mph to visit a nearby town. The cyclist averaged 18 mph on the return trip. If the round trip took 4.9 hours, find the distance to the nearby town.

Answer
Let s be the time it takes going out to the town and let t be the time for the return trip.

He travels at 24 mph out to the town, so the distance to the town is 24s miles.

He travels 18mph coming back, so the distance traveled coming back is 18t miles.

The distance traveled going out is the same as the distance coming back , so

24s = 18t.

The total time for the round trip is 4.9 hours,
so s+t = 4.9

Solve the two equations

s+t = 4.9
24s = 18t

divide both sides of 24s = 18t by 6 to get 4s = 3t , then divide both sides by 4 and get s = (3/4)t

Substitute s=(3/4)t into s + t = 4.9 and get

(3/4)t + t = 4.9

multiply through by 4 to eliminate the fraction
and get

3t + 4t = 19.6

7t = 19.6

t = 2.8 hours

The time traveling back from the town is 2.8 hours

Since he travels 18 mph coming back , the distance will be

(18)(2.8) = 50.4 miles

The town is 50.4 miles away.