SOLUTION: Airplane A travels 1400km at a certain speed. Plane B travels 1000km at a speed 50 km/h faster than plane A in 3 hrs less time. Find the same speed of each plane.
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Question 766914: Airplane A travels 1400km at a certain speed. Plane B travels 1000km at a speed 50 km/h faster than plane A in 3 hrs less time. Find the same speed of each plane. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Airplane A travels 1400km at a certain speed.
Plane B travels 1000km at a speed 50 km/h faster than plane A in 3 hrs less time.
Find the same speed of each plane.
:
let s = Plane A's speed
then
(s+50) = B's speed
:
Write a time equation; time = dist/speed
:
A's time - B's time = 3 hrs - = 3
multiply by s(s+50), resulting in:
1400(s+50) - 1000s = 3s(s+50)
1400s + 70000 - 1000s = 3s^2 + 150s
Combine to form a quadratic equation on the right
0 = 3s^2 + 150s - 400s - 70000
3s^2 - 250s - 70000
Factors to
(3s + 350)(s - 200)
We only want the positive solution here
s = 200 mph is the speed of A
:
:
Check this, find the time of each plane
1400/200 = 7 hrs
1000/250 = 4 hrs
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time dif: 3 hrs
