Question

A turbo-jet flies 50 mph faster than a super-prop plane. If a turbo-jet goes 2000 miles in 3 hours less time than it takes the super-prop to go 2800 miles, find the speed of each plane.

I do not understand how to do this at all. Please explain as well as you can! Thanks.

Answer 1

LEt v be the velocity of the turbo plane, then v-50 is the velocity of the slower. Let t be the time for turbo to go 2000 miles, then t+3 is the time for super .

(velocity*time)= distance
(v-50)(t+3)=2800
and
v*t=2000

From the second equation, t=2000/v, put that into the first equation.
(v-50)(2000/v + 3)=2800
multiply both sides by v
(v-50)(2000+3v)=2800v
multiply it all out, gather terms, and use the quadratic equation.

Answer 2

turbo-jet: 400mph
super-prop: 350mph