fritz drives to work his trip takes 30 minutes. When he takes the train it takes 20 minutes. Find the distance fritz travels to work if the train travels an average of 12 mph faster than his driving.

Question

The train and the car drive the same distance.

Answer 1

let d is the driving speed then we have distance=30d

let t is the train speed then we have distance=20t so 30d=20t(1)

since the speed we have is mph we turn it to miles per minute so the 12 mph the train runs faster than

the car 12/60 = 1/5 = 0.2 miles per min (mpm)

we have according the story; t-d=0.2 mpm so t=0.2+d plugging this value to (1) we get 30d=20(0.2+d)

deviding by 10 both sides we get 3d=2(0.2+d)  -->>>  3d=0.4+2d  , 3d-2d=0.4 so d=0.4 mpm

and because t-d=0.2  we get t=0.2+d   t=0.2 + 0.4 = 0.6 mph and plugging these values to (1) we get

30(0.4)=20(0.6) = 12 miles that is the distance