SOLUTION: A car made a journey of 144 miles, stopping for one hour along the way. Had it travelled at an average speed 4 mph faster and stopped for one and a half hours, it would have taken

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Question 1021896: A car made a journey of 144 miles, stopping for one hour along the way. Had it travelled at an average speed 4 mph faster and stopped for one and a half hours, it would have taken the same time.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A car made a journey of 144 miles, stopping for one hour along the way.
Had it travelled at an average speed 4 mph faster and stopped for one and a half hours, it would have taken the same time.
:
let s = actual speed
then
(s+ 4) = the faster speed
:
Write time equation; time dist/speed
144%2Fs + 1 = 144%2F%28%28s%2B4%29%29 + 1.5
subtract 1 from both sides
144%2Fs = 144%2F%28%28s%2B4%29%29 + .5
multiply the equation by s(s+4)
s(s+4)*144%2Fs = s(s+4)*144%2F%28%28s%2B4%29%29 + .5s(s+4)
cancel the denominators
144(s+4) = 144s + .5s^2 + 2s
144s + 576 = 144s + .5s^2 + 2s
subtract 144s from both sides
576 = .5s^2 + 2s
Form a quadratic equation on the right
0 = .5s^2 + 2s - 576
Use the quadratic formula;
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=.5; b=2; c=-576
s+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A.5%2A-576+%29%29%2F%282%2A.5%29+
You can do the math, I got a positive solution of
s = 32 mph
:
:
:
See if the checks out in the original equation
144%2F32 + 1 = 144%2F36 + 1.5
4.5 + 1 = 4 + 1.5