rate/distance/time problem

Question

You can run 250 meters per minute downhill and 180 meters per minute uphill. One day you run a total of 1557 meters in 7.6 minutes on a route that goes both uphill and downhil.  Find the number of meters you ran uphill and the number of meters you ran downhil.

Answer 1

distance = rate*time  ...  d = rt

If we run x minutes downhill, we run 7.6-x minutes uphill:

 

1557 = 250x + 180(7.6-x)

1557 = 250x + 1368 - 180x

1557 - 1368 = 70x

 

70x = 189

x = 2.7 minutes downhill

7.6-2.7 = 4.9 minutes uphill

 

Downhill:  250(2.7) = ______ meters

Uphill:  180(4.9) = ______ meters