SOLUTION: A man traveling 40 miles finds that by traveling one more mile per hour he would make a journey in 2 hours less time. How many miles per hour did he actually travel?

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Question 198446: A man traveling 40 miles finds that by traveling one more mile per
hour he would make a journey in 2 hours less time. How many miles
per hour did he actually travel?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A man traveling 40 miles finds that by traveling one more mile per
hour he would make a journey in 2 hours less time.
How many miles per hour did he actually travel?
:
Let s = mph he actually traveled
:
Write a time equation: Time = dist%2Fspeed
:
Actual time - faster time = 2 hrs
40%2Fs - 40%2F%28%28s%2B1%29%29 = 2
Multiply each term by s(s+1); results:
40(s+1) - 40s = 2s(s+1)
:
40s + 40 - 40s = 2s^2 + 2s
Arrange as a quadratic equation, (40s's cancel)
2s^2 + 2s - 40 = 0
Simplify, divide by 2
s^2 + s - 20 = 0
Factors to
(s-4)(s+5) = 0
The positive solution
s = 4 mph, actual speed
then
5 mph is the faster speed
;
Check solution find the times
40/4 = 10 hrs
40/5 = 8 hrs