Question

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

Recall your d = rt, distance = rate * time

so, let's say Fritz travel by Car at a speed of "r", if the Train runs faster then his car, then the Train runs at "r+32".

Bear in mind that, he travels from home to work by Car or Train, so, the distance if the same for either vehicle, let's say is "d" miles.

$\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{minutes}{time}\\ &-----&-----&-----\\ Car&d&r&36\\ Train&d&r+32&20 \end{array} \\\\\\ \begin{cases} \boxed{d}=36r\\ d=20(r+32)\\ ----------\\ \boxed{36r}=20(r+32) \end{cases} \\\\\\ \cfrac{36r}{20}=r+32\implies \cfrac{9r}{5}=r+32\implies 9r=5r+160 \\\\\\ 4r=160\implies r=\cfrac{160}{4}\implies \boxed{r=40}$

so... he travels at 40mph for 36 minutes, now, 36minutes is not even an hour, is 36/60 or 3/5 hr, so...    $\bf 40\cdot \cfrac{36}{60}\implies 40\cdot \cfrac{3}{5}\implies \stackrel{miles}{24}$