Maria can ride her bike to the library in 20 minutes. The trip home, wich is all uphill, takes her half an hour . If her rate is 8 miles per hour slower on the

Question

Maria can ride her bike to the library in 20 minutes. The trip home, wich is all uphill, takes her half an hour . If her rate is 8 miles per hour slower on the return trip, how far does she live from the library?

Answer 1

20 minutes = 1/3 hour

 

Let x = speed (in miles per hour) going to the library

 

Then, x - 8 = speed (in miles per hour) going home from the library

 

Distance = (Rate)(Time)

 

Since the one way distances are the same, (1/3)x = (1/2)(x-8)

 

Multiply through by the LCD, 6, to get 2x = 3(x-8)

 

                                                       2x = 3x - 24

 

                                                        x = 24 mph

 

One way distance = (1/3)x = 8 miles

 

Answer 2

Let x = the rate to the library

x * 1/3 = (x -8) * 1/2

x/3 = x/2 - 4

2x = 3x - 24

x = 24 miles / hour

 

Distance = rate * time = 24 * 1/3 = 8miles

 

Check your answer by verify the distance on the way back, it should be the same

(24 - 8) * 1/2 = 8miles

 

They match.