Use a system of equations to solve the following problem

Question

A private jet flies the same distance in 4 hours that a commercial jet flies in 3 hours. If the speed of the commercial jet was 168 mph less than 2 times the speed of the private jet, find the speed of each jet

Answer 1

Hello, Avery,

Let P and C stand for the speeds of the Private and Commercial jets, respectively. We are told that the speed, C, is "168 less than two times the speed" P. We can write this as:

C = 2P - 168

The planes cover the same distance in two different times. We can write that distance as (Time)*(Speed) = Distance

4P is the same distance as 3C, so

4P = 3C

Now substitute the earlier definition of C into this equation:

4P = 3(2P-168)

4P = 6P - 504

-2P = -504

P = 252

Then C = 2*(252) - 188

C = 336

I hope this helps,

Bob