Question

When Fritz drives to work his trip takes 36 ​minutes, but when he takes the train it takes 20 minutes. Find the distance Fritz travels to work if the train travels an average of 32 miles per hour faster than his driving. Assume that the train travels the same distance as the car.

Answer 1

24 miles

Explanation:

First we have that the time of driving is Td=36 minutes, and the time by going in train is Tt=20 minutes, the train travels the same distance x as the car, also, we know that the speed of the train Vt=32 mil/h +Vc, where Vc is the speed of the car, since

32miles/hour=32miles/(60 min)=0.53miles/min

x=V*T, we have that

x=Vt*(20 min)=(0.53mil/min +Vc)*20 min (for the train)

solving for Vc, we have

Vc=(x/20)-0.53 (1)

but in another hand (for the car)

x=Vc*(36 min)

solving for Vc, we have

Vc=x/36 (2)

comparing equation (1) and (2) we have

(x/20)-0.53 = x/36

solving for x

16x=384

x=24 miles