when fritz drives to work his trip is 35 minutes, but when he takes the train it takes 15 minutes. find the distance fritz travels to work if the train travels 80 miles per hour faster than his driving.

Let driving speed of Fritz = X miles per hour

so train speed = X+80 miles per hour

Train travels for 15 minutes = 15/60 = 1/4 hours

Distance travelled by train = speed x time = (X+80) x 1/4 = (X+80)/4 = (X/4 +20) miles

Fritz travels for 35 minutes = 35/60 = 7/12 hours

Distance travelled by fritz in 35 minutes = speed x time = X x 7/12 = 7X/12 miles

Now distance travelled by train = distance driven by Fritz

X/4 + 20 = 7X/12

X/4 + 20 - X/4 = 7X/12 - X/4

20 = 7X/12 - (X/4)x(3/3) = 7X/12-3X/12

20 = (7-3)X/12 = 4X/12 = X/3

20 x 3 = (X/3) x 3

X = 60 miles/jour

Distance travelled by Fritz to work = 7X/12=7x60/12 = 35 miles

**Let us check the answer**

Distance travelled by train = speed of train x time taken by train = (60+80) x 1/4 = 140/4 = 35 miles

so distance travelled by train = distance driven by Fritz **(Answer is verified)**