Find the Distance

Question

When Fritz drives to work his trip takes 35 minutes, but when he takes the train it takes 15 minutes. Find the distance Fritz travels to work if the train travels an average of 80 miles per hour faster than his driving. Assume that the train travels the same distance as the car. 

Answer 1

Let D be the distance and S Fritz's speed in mph.

Then, for Fritz, D miles = S miles/1 hour * 1 hour/60 minutes * 35 minutes = 35S/60 = 7/12 S miles

For the train , D miles =  (S+80) miles/1 hour * 1 hour/60 minutes * 15 minutes = 15(S+80)/60 = (S+80)/4 miles

So, 7/12 S = (S+80)/4

Solve for S to get Fritz's speed and then you can calculate the distance.