SOLUTION: A motorist made a 200 km trip averaging 50 km/h on a level road and 25 km/h on a mountain road. The time spent on the mountain road was 1 hour less than the time spent on the level

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: A motorist made a 200 km trip averaging 50 km/h on a level road and 25 km/h on a mountain road. The time spent on the mountain road was 1 hour less than the time spent on the level      Log On


   

Question 944311: A motorist made a 200 km trip averaging 50 km/h on a level road and 25 km/h on a mountain road. The time spent on the mountain road was 1 hour less than the time spent on the level road. How many km of the trip were on the mountain road?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A motorist made a 200 km trip averaging 50 km/h on a level road and 25 km/h on a mountain road.
The time spent on the mountain road was 1 hour less than the time spent on the level road.
How many km of the trip were on the mountain road?
:
Let m = distance on mountain roads
then since the total distance is 200km,
(200-m) = distance on level roads.
:
Write a time equation, time = dist/speed
:
level road time - mountain road time = 1 hr
%28%28200-m%29%29%2F50 - m%2F25 = 1
multiply equation by 50 and cancel the denominators, leaving us with:
200-m - 2m = 50
-3m = 50 - 200
-3m = -150
m = -150/-3
m = +50 km on mountain roads
:
:
Confirm this by finding the time of each, level road: 200-50 = 150 km
150%2F50 - 50%2F25 =
3 - 2 = 1 hr