SOLUTION: Arif walks for x hours at 5km/h and runs for y hours at 10km/h. He travels a total of 35km and his average speed is 7km/h. Find the value of x and y. I have worked out that di

Algebra ->  Equations -> SOLUTION: Arif walks for x hours at 5km/h and runs for y hours at 10km/h. He travels a total of 35km and his average speed is 7km/h. Find the value of x and y. I have worked out that di      Log On


   

Question 622109: Arif walks for x hours at 5km/h and runs for y hours at 10km/h. He travels a total of 35km and his average speed is 7km/h. Find the value of x and y.
I have worked out that distance divided by speed = time which is 5 hours but got stuck from there - not sure how to divide the walking and running so that the average speed = 7km/h.
Thanks in advance.
Found 2 solutions by Alan3354, jessica43:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Arif walks for x hours at 5km/h and runs for y hours at 10km/h. He travels a total of 35km and his average speed is 7km/h. Find the value of x and y.
---------------
5x + 10y = 35 (distance) --> x + 2y = 7
t = d/r = 35/7 = 5 hours
x + y = 5
x + 2y = 7
---------------- Subtract
-y = -2
y = 2
x = 3

Answer by jessica43(140) About Me  (Show Source):
You can put this solution on YOUR website!
To solve this problem, you need to write two equations using what you know.
First, you know that Arif walks for x hours at 5km/h and runs for y hours at 10km/h for a total of 35 km. Like you stated, distance equals time multiplied by speed, so we need to create one equation adding the distances from running and walking that will total 35km. This can be written as:
5x + 10y = 35
(where 5x is the total distance walking and 10y is the total distance running)
Next, you know that the average speed is 7km/h. Using the equation speed = distance/time, we have:
7 = 35/(x+y)
Now rewrite this second equation in terms of x:
7 = 35/(x+y)
7(x+y) = 35
7x + 7y = 35
7y = 35 - 7x
y = 35/7 - 7x/7 (I am just simplifying by dividing both sides by 7)
y = 5 - x
Now plug this second equation into the first equation for y, and solve for x:
5x + 10y = 35
5x + 10(5-x) = 35
5x + 50 - 10x = 35
50 - 5x = 35
-5x = -15
x = 3
So Arif walked for 3 hours. To find y, plug this x value into the second equation:
y = 5 - x
y = 5 - 3
y = 2
So x = 3 and y = 2.