SOLUTION: Need to find the equations for x in this word problem. Thanks! Jim made a 450 mile trip in his car at a certain speed. If he ha d gone 10 mph faster, he could have made the tr

Algebra ->  Equations -> SOLUTION: Need to find the equations for x in this word problem. Thanks! Jim made a 450 mile trip in his car at a certain speed. If he ha d gone 10 mph faster, he could have made the tr      Log On


   

Question 311465: Need to find the equations for x in this word problem. Thanks!

Jim made a 450 mile trip in his car at a certain speed. If he ha
d 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 450 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 = that "certain speed"
then
(s+10) = the faster speed
:
Write a time equation; time = dist/speed
:
Actual time - faster time = 1 hr
450%2Fs - 450%2F%28s%2B10%29 = 1
multiply by s(s+10), results
450(s+10) - 450s = s(s+10)
:
450s + 4500 - 450s = s^2 + 10s
Arrange as quadratic equation on the right
0 = s^2 + 10s - 4500
Use the quadratic formula to find s
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this problem x=s, a=1, b=10 c=-4500
s+=+%28-10+%2B-+sqrt%2810%5E2-4%2A1%2A-4500+%29%29%2F%282%2A1%29+
:
s+=+%28-10+%2B-+sqrt%28100+%2B+18000+%29%29%2F%282%29+
:
s+=+%28-10+%2B-+sqrt%2818100+%29%29%2F%282%29+
Two solutions, but we just want positive solution
s+=+%28-10+%2B+134.536%29%2F%282%29+
s = 124.536%2F2
s = 62.27 mph his actual speed
:
:
Check solution, find the time at each speed
450/62.27 = 7.2266 hrs
450/72.27 = 6.2266 hrs
--------------------------
difference: 1 hrs