SOLUTION: A student travelled for X hours at 5km/hr and for Y hours at 10km/hr. The journey was 35 km altogether, find XandY if the average speed for the journey was 7 km/hr

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Question 767494: A student travelled for X hours at 5km/hr and for Y hours at 10km/hr. The journey was 35 km altogether, find XandY if the average speed for the journey was 7 km/hr
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Make a data table.

_____________________speed__________time____________distance
_____________________5______________x______________(___)
_____________________10_____________y______________(___)
TOTAL________________|____________x+y______________35


We want to solve for x and y somehow. First we could fill in the distance expressions, in case it helps sooner in the process:

_____________________speed__________time____________distance
_____________________5______________x______________(5x)
_____________________10_____________y______________(10y)
TOTAL________________|____________x+y______________35

We must try to do something with the average speed reported of 7 km/hr.
Total distance compared to total time should be this average:
35%2F%28x%2By%29=7
5%2F%28x%2By%29=1
x%2By=5

We also have a distance equation about total distance traveled:
5x%2B10y=35
x%2B2y=7

Solve the system for x and y:
x%2By=5 and x%2B2y=7
Subtract first from second.
0%2By=7-5
____________________________________________
ANSWER:___________y=2 so x=3____________
____________________________________________
ANSWER: 3 hours at 5 km/h and 2 hours at 10 km/h