total distance between friend living place

Question

Aya rode her bicycle from her house to her friends house averaging 16km/h. Her friend drove her back home at a speed of 80 km/h. If her total traveling time was 3 hours, how far did her friend live?

Answer 1

Let's call the distance from Aya's house to her friends house D.

The distance back has to be the same, right? Now let's consider the times for each part. The total time is 3 hours, so the sum of the 2 legs of the trip have to total to 3.

 

T_out + T_back = 3

 

The distance there is

 

V_out * T_out = D

 

The distance back is the same, but using the 'back' time and speed.

 

V_back * T_back = D

 

Since both of these are equal to D, we can set them equal to each other

 

V_out * T_out = V_back * T_back

 

Now we look back at the time equation and solve for T_out 

 

T_out = 3 - T_back

 

Plug all our given info in

 

16 * T_out = 80 * (3 - T_out)

16T = 240 - 80T

96T = 240

T = 240/96

T = 2.5 hours, this is the time it takes to go to Aya's friend's house.

 

To fin the distance, we look back and pick one of our distance equations and plug this time into it. We should pick the first one because it is a little easier.

 

V_out * T_out = D

16 * 2.5 = D

40 km = D

 

The distance between their houses is 40 km.

 

I hope this helps! Please ask any questions if you have them.