<PRE><B>Question 144782</B>
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 = speed of his vehicle
then
(s+10) = the faster speed
:
Write a time equation: Time = {{{dist/speed}}}
:
Actual time - 1 hr = Faster speed time
{{{200/s}}} - 1 = {{{200/((s+10))}}}
:
Multiply equation by s(s+10)
s(s+10)*{{{200/s}}} - s(s+10)(1) = s(s+10)*{{{200/((s+10))}}}:
Cancel the denominators:
:
200(s+10) - s(s+10) = 200s
:
200s + 2000 - s^2 - 10s = 200s
:
0 = s^2 + 10s + 200s - 200s - 2000
:
A quadratic equation
s^2 + 10s - 2000 = 0
:
Factors to:
(s+50)(s-40) = 0
:
Positive solution
s = 40 mph
:
:
Check solution by finding the times:
200/40 = 5 hrs
200/50 = 4 hrs


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