Quadratic function help?

Question

Solve:
A turbo-jet flies 50 mph faster thana super-prop plane. If a turbo-jet goes 2000 mi. in 3 hr less than it takes the super-prop to go 2800 mi. find the speed of each plane.

Answer 1

Let J be the speed of the turbo-jet and S the speed of the super-prop. Also note that velocity * time = distance.

"A turbo-jet flies 50 mph faster than a super-prop plane"

J = S + 50

"If a turbo-jet goes 2000 miles in 3 hours less than it takes the super-prop to go 2800 miles, find the speed of each."

The time for the super-prop to go 2800 miles is T

T = 2800 / S

Now for the turbo-jet:

T - 3 = 2000 / J

You now have three equations in three unknowns:

J = S + 50
T = 2800 / S
T - 3 = 2000 / J

Let's rewrite these as

J = S + 50
S = 2800 / T
J = 2000 / ( T - 3 )

Substitute the middle expression for S into the first equation to get

J = 2800 / T + 50

Then set the first and third equations equal to each other

2800 / T + 50 = 2000 / ( T - 3 )

Solve this equation for T; then you can easily find J and S.