SOLUTION: A car traveled 960 miles at a certain speed. If the speed had been 12 mph faster, the trip could have been made in 4 hours less time. Find the speed.

Question 949051: A car traveled 960 miles at a certain speed. If the speed had been 12 mph faster, the trip could have been made in 4 hours less time. Find the speed.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A car traveled 960 miles at a certain speed.
If the speed had been 12 mph faster, the trip could have been made in 4 hours less time.
Find the speed.
:
Let s = the speed
:
Write a time equation; time = dist/speed
:
normal time - faster time = 4 hrs
- = 4
multiply equation by s(s+12)
960(s+12) - 960s = 4s(s+12)
960s + 11520 - 960s = 4s^2 + 48s
Combine to form a quadratic equation on the right
0 = 4s^2 + 48s - 11520
simplify, divide by 4
s^2 + 12s - 2880 = 0
You can use the quadratic formula; a=1; b=12; c=-2880, but this will factor
(s+60)(s-48) = 0
The positive solution is all we want here
s = 48 mph is the speed of the car
:
:
Check this, find the times at each speed
960/48 = 20 hrs
960/60 = 16 hrs
---------------
differ by: 4 hrs
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