Math problem involving distance and speed and time?

Question

When fritz drives to work his trip takes 36 minutes, but when he takes the train ut tajes 20 minutes. Find the distance fritz travels to work if the train travels an average of 32 miles per hour faster than his driving.

Fritz travles ??? miles to work

Answer 1

Distance=Speed x Time

20 minutes = 1/3 hour

36 minutes = 3/5 hour

Let C = Speed Of Car in mph

Let T = Speed Of Car in mph = C+32

(3/5)(C) = (1/3)(C+32)

Solving this yields, C=40 mph

Distance = (40 mph)(3/5 hr) = 24 miles.

Answer 2

Car Speed = d/(36/60)

Train speed = Car Speed + 32 = d/(20/60)

Subtract the two equations

-32 = d/(36/60) - d/(20/60)  mph

-32 = 60d/36 - 60d/20

-32 = (1200d - 2160d) / 720

-32 = - 960d / 720 mph

-32 x 720 = -960d mph

d = -32 x 720 / -960 = 24 miles

Answer 3

time = distance / speed

or distance = time * speed

let the driving speed be x

then the train speed is x + 32

36 minutes = .6 hour

20 minutes = .3333 hour = 1/3 hour

since the distance is the same either way, then time * speed must equate for driving and the train

.6(x) = (1/3)(x + 32)

.6x = (1/3)x + 32/3

multiply by 3

1.8x = x + 32

.8x = 32

x = 32/.8 = 40

so the driving speed is 40 mph and the train speed is 72 mph

40 * .6 = 24 miles

72 * 1/3 = 24 miles

he travels 24 miles to work at either 40 mph (driving) or 72 mph (train)