SOLUTION: Imogene's car traveled 450 miles at certain speed. If car had gone 5 mph faster, the trip would have taken 1 hour less, find average speed

Question 1046818: Imogene's car traveled 450 miles at certain speed. If car had gone 5 mph faster, the trip would have taken 1 hour less, find average speed
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Imogene's car traveled 450 miles at certain speed.
If car had gone 5 mph faster, the trip would have taken 1 hour less,
find average speed'
:
let s = the actual speed
then
(s+5) = the faster speed
:
write a time equation, time = dist/speed
Original time - faster speed time = 1 hr
- = 1
multiply eq by s(s+5)
s(s+5)* - s(s+5) = 1s(s+5)
cancel the denominators and you have
450(s+5) - 450s = s(s+5)
distribute
450s + 2250 - 450s = s^2 + 5s
form a quadratic equation on the right
0 = s^2 + 5s - 2250
You can use the quadratic formula to find s; a=1; b=5; c=-2250
But this will factor to
(s+50)(s-45) = 0
the positive solution is what we want
s = 45 mph is his average speed.
:
:
Check this by finding the actual time at each speed
450/45 = 10 hrs
450/50 = 9 hrs
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