SOLUTION: Larry's time to travel 250 miles is 2 hours more than Terrell's time to travel 165 miles. Terrell drove 5 miles per hour faster than Larry. How fast did each one travel?

Question 706882: Larry's time to travel 250 miles is 2 hours more than Terrell's time to travel 165 miles. Terrell drove 5 miles per hour faster than Larry. How fast did each one travel?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Larry's time to travel 250 miles is 2 hours more than Terrell's time to travel 165 miles.
Terrell drove 5 miles per hour faster than Larry.
How fast did each one travel?
:
Let s = L's speed
then
(s+5) = T's speed
:
Write a time equation; time = dist/speed
:
L's time - T's time = 2 hrs
- = 2
multiply by s(s+5) to clear the denominators, resulting in
250(s+5) - 165s = 2s(s+5)
:
250s + 1250 - 165s = 2s^2 + 10s
:
85s + 1250 = 2s^2 + 10s
Combine on the right to form a quadratic equation
0 = 2s^2 + 10s - 85s - 1250
0 = 2s^2 - 75s - 1250
You can use the quadratic formula here, but this will factor to
(2s + 25)(s - 50) = 0
The positive solution is all we want here
s = 50 mph is L's speed
you can find T's speed
:
Check your solutions by finding the actual travel times of each.
See that they differ by 2 hrs

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