SOLUTION: A car traveled from city X to city Y at a uniform speed of 120 miles/ hr. The car then travels from city Y to city Z at a uniform speed of eof 100miles/ hr. If the distance the car
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Question 987684: A car traveled from city X to city Y at a uniform speed of 120 miles/ hr. The car then travels from city Y to city Z at a uniform speed of eof 100miles/ hr. If the distance the car travelled city X and Y is twice the distance the car travelled between city Y and Z , what is the average speed in miles per hour the car travelled between city X and Z
Many thanks for your help
Manoj
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A car traveled from city X to city Y at a uniform speed of 120 miles/ hr.
The car then travels from city Y to city Z at a uniform speed of of 100miles/ hr.
If the distance the car travelled city X and Y is twice the distance the car travelled between city Y and Z , what is the average speed in miles per hour the car travelled between city X and Z
:
let a = the average speed of the whole trip
let d = the distance from y to z
we know the dist from x to y, is twice the dist from y to z, therefore
2d = the distance from x to y
and
3d = the total distance from x to z
:
Write a time equation, time = dist/speed
xy time + yz time = total time
+ =
multiply by 600a
600a* + 600a* = 600a*
Cancel the denominators
5a(2d) + 6ad = 600(3d)
10ad + 6ad = 1800d
16ad = 1800d
simplify divide both sides by d
16a = 1800
a = 1800/16
a = 112.5 mph av speed for x to z
:
:
We can confirm this by choosing a value for d, say 100 mi, and finding the times
+ =
1.67 + 1 = 2.67
:
Equation will be correct for any value of d
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