find the speed of each jet?

Question

A private jet flies the same distance in 15 hours that a commercial jet flies in 12 hours. If the speed of the commercial jet was 174 mph less than 2 times the speed of the private jet, find the speed of each jet.

Answer 1

Let R = the rate of the private jet

Then 2R - 174 is the rate of the commercial jet (174 less then twice the rate of the private jet)

The jets travel the same distance, but in different amounts of time. Since distance equals rate times time (D=RT), if we can come up with expressions for the distance travelled by each, those expressions can be set equal to each other.

For the private jet:

T = 15 hours

R represents its rate, so the distance covered is:

D_private=15R

For the commercial jet.

T = 12 hours

Rate is (2R - 174)

D_commercial= 12(2R - 174)

And those distances are known to be equal. Finally we have our equation:

15R = 12(2R - 174)

15R = 24R - 12(174)

12(174) = 24R - 15R

9R = 12(174)

R = 12(174)/9

R = 4(58) = 232 mph

2R - 174 = 2(232) - 174 = 290 mph

Check:

Private:

15(232)=3480 mi

Commercial:

12(290) = 3480 mi