SOLUTION: A relay race required runners to run from Point A to Point B and then back to point A. the distance from A to B = 22km.
On the return trip (Point B to Point A) the runners avera
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On the return trip (Point B to Point A) the runners avera
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Question 466759: A relay race required runners to run from Point A to Point B and then back to point A. the distance from A to B = 22km.
On the return trip (Point B to Point A) the runners average speed decreased by (1.2km/hr).
If the relay took 10.5 hours to complete, what was the average speed from Point A to Point B.
Thank You Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A relay race required runners to run from Point A to Point B and then back to point A. the distance from A to B = 22km.
On the return trip (Point B to Point A) the runners average speed decreased by (1.2km/hr).
If the relay took 10.5 hours to complete, what was the average speed from Point A to Point B.
:
Let s = av speed from Point A to B
:
It says,"On the return trip (Point B to Point A) the runners average speed decreased by (1.2km/hr)." therefore:
(s-1.2) = return trip speed (B to A)
:
Write a time equation; time = dist/speed + = 10.5
;
Multiply by s(s-1.2), results:
22(s-1.2) + 22s = 10.5s(s-1.2)
:
22s - 26.4 + 22s = 10.5s^2 - 12.6s
:
44s - 26.4 = 10.5s^2 - 12.6s
:
0 = 10.5s^2 - 12.6s - 44s + 26.4
:
A quadratic equation
10.5s^2 - 56.6s + 26.4 = 0
;
Multiply by 10 to get rid of the decimals
105s^2 - 566s + 264 = 0
:
Use the quadratic formula to solve this
a=105, b=-566, c=264, s=x
:
:
Two solutions, but only this one will make sense
s =
s = 4.87 km/hr, av speed from A to B
:
:
Check this by finding the times
22/4.87 = 4.5 hrs
22/3.67 = 6.0 hrs
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tot time: 10.5 hrs, confirms our solution
