SOLUTION: A pilot flies a distance of 600 miles. He could fly the same distance 24 minutes less time by increasing his average speed by 50 mph. Find his actual average speed.

Question 763886: A pilot flies a distance of 600 miles. He could fly the same distance 24 minutes less time by increasing his average speed by 50 mph. Find his actual average speed.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A pilot flies a distance of 600 miles.
He could fly the same distance 24 minutes less time by increasing
his average speed by 50 mph.
Find his actual average speed.
:
Let s = the actual speed
then
(s+50) = the faster speed
:
change 24 min to .4 hrs
:
Write a time equation; time = dist/speed
Actual time - faster time = .4 hr
- = .4
multiply eq by s(s+50), resulting in:
600(s+50) - 600s = .4s(s+50)
:
600s + 30000 - 600s = .4s^2 + 20s
Combine as a quadratic equation on the right
0 = .4s^2 + 20s - 30000
multiply equation by 2.5 to get a coefficient of s^2 to equal 1
and try to factor, to avoid the tedious quadratic formula.
s^2 + 50s = 75000
Factors to
(s+300)(s-250)= 0
The positive solution
s = 250 mph is the actual speed
:
:
Check this by finding the times at each speed
600/250 = 2.4 hrs
600/300 = 2.0 hrs
-------------------
difference .4 hrs which is 20 min less

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