SOLUTION: I need help with this question Jim made a 350 mile trip in his car at a certain speed. If he had gone 10 mph faster, he could have made the trip in one hour less time. Find hi

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Question 275068: I need help with this question
Jim made a 350 mile trip in his car at a certain speed. If he had gone 10 mph faster, he could have made the trip in one hour less time. Find his speed.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Jim made a 350 mile trip in his car at a certain speed.
If he had gone 10 mph faster, he could have made the trip in one hour less time.
Find his speed.
:
Let s = his speed
then
(s+10) = the faster speed
:
Write a time equation; time = dist/speed
:
Actual time - faster time = 1 hr
350%2Fs = 350%2F%28%28s%2B10%29%29 = 1
:
Multiply equation by s(s+10); results:
350(s+10) - 350s = s(s+10)
:
350s + 3500 - 350s = s^2 + 10s
combine and arrange as quadratic equation
s^2 + 10s - 3500 = 0
use the quadratic formula to find s
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x = s; a=1; b=1-; c=-3500
s+=+%28-10+%2B-+sqrt%2810%5E2-4%2A1%2A-3500+%29%29%2F%282%2A1%29+
:
s+=+%28-10+%2B-+sqrt%28100+-+%28-14000%29%29%29%2F2+
:
s+=+%28-10+%2B-+sqrt%2814100%29%29%2F2+
the positive solution
s+=+%28-10+%2B+118.74%29%2F2+
:
s = 108.74%2F2
s = 54.37 mph is the actual speed
:
:
Check solution by finding the times
350/54.37 = 6.4 hrs
350/64.37 = 5.4 hrs, one hr difference