SOLUTION: A cyclist rides over a hill , a total journey of 9km. His average speed uphill is 8km/hr and his average speed downhill is 20km/hr . If the journey takes 45minutes , find the dista
Algebra ->
Finance
-> SOLUTION: A cyclist rides over a hill , a total journey of 9km. His average speed uphill is 8km/hr and his average speed downhill is 20km/hr . If the journey takes 45minutes , find the dista
Log On
Question 1201528: A cyclist rides over a hill , a total journey of 9km. His average speed uphill is 8km/hr and his average speed downhill is 20km/hr . If the journey takes 45minutes , find the distance he rode uphill.( the answer is 4km)
Now , this is how I worked it out :
I took 8 km/hr and 9km and divided them (since time=distance/speed)
so 9/8hrs he took uphill. and then I did 8km/hr multiplied by 9/8hrs which is 9.
so distance uphill which is 9cm . but that is the total journey given . How do you work this out please? Answer by ikleyn(52781) (Show Source):
You can put this solution on YOUR website! .
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.
~~~~~~~~~~~~~~~~~~
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.
+----------------------------------------------+
| At this point, the setup is done. |
| Now your task is to solve the equation. |
+----------------------------------------------+
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 !
