Question 172465: Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip
would have taken 1 hour less. Find the speed of his vehicle.
:
Let s = original speed of the vehicle
then
(s+10) = the faster speed
:
Write a time equation, time =
:
original time = faster time + 1 hour = + 1
:
Multiply equation by s(s+10)
s(s+10)* = s(s+10)* + s(s+10)
Results:
200(s+10) = 200s + s^2 + 10s
:
200s + 2000 = 200s + s^2 + 10s
:
Arrange as quadratic equation:
s^2 + 10s + 200s - 200s - 2000 = 0
:
s^2 + 10s - 2000 = 0
Factors to:
(s + 50)(x - 40) = 0
:
s = + 40 mph is the original speed
:
:
Check solution by finding the times
200/40 = 5 hrs
200/50 = 4 hrs
