Question

A commercial jet and a private airplane fly from Denver to Phoenix. It takes the commercial jet 1.1 hours for the flight, and it takes the private airplane 1.8 hours. The speed of the commercial jet is 210 miles per hour faster than the speed of the private airplane. Find the speed of both airplanes.

Answer 1

Speed of private airplane = 330 mph

Speed of commercial jet = 540 mph

Explanation:

Let the distance between Denver to Phoenix be s, speed of private airplane be u and speed of commercial jet be v.

We have the speed of the commercial jet is 210 miles per hour faster than the speed of the private airplane

That is v = u + 210 ------ eqn 1

It takes the commercial jet 1.1 hours for the flight from Denver to Phoenix.

`s=1.1* v=1.1v`

It takes the private airplane 1.8 hours for the flight from Denver to Phoenix.

`s=1.8* u=1.8u`

So we have

1.1 v = 1.8 u

v = 1.636 u

Substituting in eqn 1

1.636 u = u + 210

0.636 u = 210

u = 330 mph

v = 330 + 210 = 540 mph

Speed of private airplane = 330 mph

Speed of commercial jet = 540 mph

Answer 2

The speed of the private airplane is 770 mph, the speed of the commercial airplane is 980 mph.

Explanation:

Let x mph be the speed of private airplane. If the speed of the commercial jet is 210 miles per hour faster than the speed of the private airplane, then the speed of commercial airplane is (x+210) mph.

It takes the commercial jet 1.1 hours for the flight, then it covered the distance of

`1.1(x+210)\ miles`

It takes the private airplane 1.8 hours for the flight, then it covered the distance of

`1.8x\ miles.`

The distances are the same, so

`1.1(x+210)=1.8x\\ \\1.1x+231=1.8x\\ \\1.8x-1.1x=231\\ \\0.7x=231\\ \\7x=2,310\\ \\x=770`

The speed of the private airplane is 770 mph, the speed of the commercial airplane is 770 + 210 = 980 mph.