Question 125482
Use the distance = rate times time formula, {{{d=rt}}}


Since we are trying to find the rate for the plane out of the jet stream, let that rate be r.  Then we know that the rate while in the jet stream must be r + 80.


The distance traveled while in the jet stream, d, must be equal to the rate while in the jet stream times the 5 hours that it flew in the jet stream, or:


{{{d=5(r+80)}}}


The distance traveled while out of the jet stream is 550 miles less than the distance traveled in the jet stream, so we can express that distance as {{{d-550}}}, but we can also express this distance as r, the rate out of the jet stream times 4, the number of hours flown out of the jet stream, or:


{{{d-550=4r}}}


Re-writing the first equation we get:  {{{d=5r+400}}}, giving us an expression for d that can be substituted into the second equation:


{{{5r+400-550=4r}}}
{{{5r-150=4r}}}
{{{5r-4r=150}}}
{{{r=150}}}, the speed of the aircraft out of the jet stream.


Check the answer.

If the speed out of the jet stream is 150, then the speed in the jet stream must be 230.  230 times 5 = 1150, so the airplane traveled 1150 miles while in the jet stream.


The speed out of the jet stream is 150, so the distance traveled out of the jet stream is 150 times 4 = 600, and 600 = 1150 - 550.  Answer checks.