SOLUTION: A plane can fly 280 miles in the same time as it takes a car to go 100 miles. If the car travels 90 mph slower than the plane, find the speed of the plane.

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Question 1143009: A plane can fly 280 miles in the same time as it takes a car to go 100 miles. If the car travels 90 mph slower than the plane, find the speed of the plane.
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
plane flies 280 miles in the same time as it takes a car to go 100 miles.
the car travels 90 miles per hour slower than the plane.
find the speed of the plane.

r * t = d
r = rate
t = time
d = distance

for the plane, r * t = d becomes x * t = 280
for the car, r * t = d becomes (x-90) * t = 100

x represents the speed of the plane.
x-90 represents the speed of the car.

t represents time in both equations because the time in both equations is the same.

in the first equation, solve for t to get t = 280 / x
in the second equation replace t with 280 / x to get (x-90) * 280/x = 100
simplify this equation to get 280 - 90 * 280 / x = 100
simplify further to get 280 - 25200 / x = 100
subtract 280 from both sides of the equation to get -25200 / x = -180
multiply both sides of the equation by x to get -25200 = -180 * x
divide both sides of the equation by -180 and solve for x to get x = -25200 / -180 = 140

the plane flies at 140 miles per hour.
the car drives at 50 miles per hour (140 - 90 = 50).
for the plane, 140 * t = 280 which gets you t = 280 / 140 = 2.
for the car, 50 * t = 100 which gets you t = 100 / 50 = 2.

both the car and the plane take 2 hours to travel their respective distances.
your solution is the speed of the plane is 140 miles per hour.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

A plane can fly 280 miles in the same time as it takes a car to go 100 miles. If the car travels 90 mph slower than the plane, find the speed of the plane.
Let speed of plane be S

Then speed of car  = S - 90

We then get the following TIME equation: matrix%281%2C3%2C+280%2FS%2C+%22=%22%2C+100%2F%28S+-+90%29%29

Cross-multiply to get: 280(S - 90) = 100S

Continue to solve for S, and you should get: