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A cyclist rides over a hill , a total journey of 9 km. His average speed uphill is 8 km/hr
and his average speed downhill is 20 km/hr. If the journey takes 45minutes, find the distance he rode uphill.
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Let x is the distance uphill, in kilometers.
Then the distance downhill is (9-x) kilometers.
The time travel uphill is hours (distance divided by the speed).
The time travel downhill is hours (due to the same reason).
The total time is 3/4 of an hour, giving you an equation
+ = of an hour.
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| At this point, the setup is done. |
| Now your task is to solve the equation. |
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For it, multiply the equation by 80 (both sides). You will get
10x + 4*(9-x) =
10x + 36 - 4x = 3*20
10x - 4x = 60 - 36
6x = 24
x = 24/6 = 4 kilometers.
ANSWER. The distance uphill is 4 kilometers.
CHECK. 0.5 of an hour is spent to travel 4 km uphill at 8 km/h.
3/4 - 1/2 = 1/4 of an hours remained.
It was spent to travel (9-4) = 5 km downhill at the speed of 20 km/h. ! correct !
Solved.
It is one of possible ways to solve the problem.
There are other ways, too.
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See the lesson
- Using time equation to solve some Travel and Distance problems
in this site. Find there the solutions for other similar (and different) problems.