SOLUTION: 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.

Algebra ->  Human-and-algebraic-language -> SOLUTION: 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.       Log On


   

Question 153517: 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) About Me  (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 = his speed
then
(s+10) = the faster speed
:
Write a time equation: Time = dist%2Fspeed
:
Actual time = Faster time - 1 hr
200%2Fs = 200%2F%28%28s%2B10%29%29 + 1
:
Multiply equation by common denominator, s(s+10); results:
200(s+10) = 200s + s(s+10)
:
200s + 2000 = 200s + s^2 + 10s
:
The 200s's are eliminated, leaving us with the quadratic equation:
s^2 + 10x - 2000 = 0
easily factors to:
(s+50)(s-40) = 0
Positive solution
s = 40 mph his speed
:
:
Check solution by finding the time of each
200/40 = 5 hrs
200/50 = 4 hrs