SOLUTION: Please help me translate into a quadratic equation and solve. Steve traveled 200 miles at a certain speed. Had he gone 10 MPH faster, the trip would have taken 1 hour less. Find

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Please help me translate into a quadratic equation and solve. Steve traveled 200 miles at a certain speed. Had he gone 10 MPH faster, the trip would have taken 1 hour less. Find      Log On


   

Question 139174: Please help me translate into a quadratic equation and solve.
Steve traveled 200 miles at a certain speed. Had he gone 10 MPH faster, the trip would have taken 1 hour less. Find the speed of his vehicle.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Steve traveled 200 miles at a certain speed. Had he gone 10 MPH faster, the trip would have taken 1 hour less. Find the speed of his vehicle.
:
Let s = his actual speed
then
(s+10) = his "if" speed
:
Write a time equation: Time = dist/speed
:
Actual time = Faster speed time + 1 hr
200%2Fs = 200%2F%28%28s%2B10%29%29 + 1
Multiply equation by s(s+10) to get rid of the denominators:
s(s+10)*200%2Fs = s(s+10)*200%2F%28%28s%2B10%29%29 + s(s+10)*1
cancel the denominators out and you have:
200(s+10) = 200s + s(s+10)
:
200s + 2000 = 200s + s^2 + 10s
:
Combine;
0 = s^2 + 10s + 200s - 200s - 2000
A quadratic equation
s^2 + 10s - 2000 = 0
Factors to:
(s+50) (s-40) = 0
The positive solution:
s = +40 mph is his speed
:
Check solution by finding the times
200/40 = 5 hrs
200/50 = 4 hrs