This question is pertaining to college algebra

Question

When Fritz drives to work his trip takes 30 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 12 miles per hour faster than his driving. Assume that the train travels the same distance as the car.

Answer 1

Let x = speed of car in miles per hour

 

Then, x + 12 = speed of train in miles/hour

 

30 minutes = 1/2 hour

 

20 minutes = 1/3 hour

 

Distance = (Rate)(time)

 

Distance of car = Distance of train

 

So, (1/2)x = (1/3)(x+12)

 

Multiply by the LCD, 6, to obtain 3x = 2(x+12)

 

                                              3x = 2x + 24

 

                                               x = 24 miles per hour

 

The speed of the car is 24 mph and the train's speed is 36 mph.