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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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.
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Answer by ankor@dixie-net.com(22740) About Me  (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
22%2Fs + 22%2F%28%28s-1.2%29%29 = 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
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=105, b=-566, c=264, s=x
s+=+%28-%28-566%29+%2B-+sqrt%28-566%5E2-4%2A105%2A264+%29%29%2F%282%2A105%29+
:
s+=+%28566+%2B-+sqrt%28320356-110880+%29%29%2F%28210%29+
:
s+=+%28566+%2B-+sqrt%28209476%29%29%2F%28210%29+
Two solutions, but only this one will make sense
s+=+%28566+%2B+457.7%29%2F%28210%29+
s = 1023.7%2F210
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
-----------------
tot time: 10.5 hrs, confirms our solution