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 48 miles per hour faster than his driving. assume that the train travels the same distance as the car?

Let t be the rate at which the train runs, and c the rate at which the car runs.

The distance is the same regardless of vehicle used. Thus, (distance traveled by train) = (distance traveled by car). Symbolically,

(20/60) (hr) * (c+48) (mph) = (36/60) (hr) * c

Multiplying both sides by 60, we get

(20) (hr) * (c+48) (mph) = (36) (hr) * c

Solve this for c, the rate at which the car travels.

(20) (c) + 960 = 36c

Subtracting 20c from both sides, we get

960 = 16c. Thus, c = 960/16 = 60.

The car travels at the rate of 60 mph and the train at (60+48) mph, or 108 mph.