An airplane flew 4 hours with a 25 mph tail wind. The return trip against the same wind took 5 hours. How do you find the speed of the airplane in still air?

2 Answers
Oct 8, 2015

Answer:

The speed of the plane is 225 mph.

Explanation:

To solve this task you can use the following system of equations:

#{(s/(v+25)=4),(s/(v-25)=5):}#

Both equations come straight from the laws of cinematics (time equals distance divided by speed)

If you multiply both equations by the denominators you will get:

#{(s=4*(v+25)),(s=5*(v-25)):}#

So you can write only one equation with the unknown #v#:

#4*(v+25)=5*(v-25)#

#4v+100=5v-125#
#5v-4v=125+100#
#v=225#

Answer: The speed of the plane without the wind is #225# mph.

Check:

First we calculate the distance:

#s=4*(225+25)=4*250=1000#

Next we check the times:

a) with the wind

#t=s/(v+25)=1000/(225+25)=1000/250=4#

b) against the wind

#t=s/(v-25)=1000/(225-25)=1000/200=5#

Oct 8, 2015

Answer:

I found #225mph#

Explanation:

Call the speed of the plane (in still air) #s_p#; you get from speed=distance/time:
#s_p+25=d/4#
and:
#s_p-25=d/5#

from the first equation:
#d=4(s_p+25)#
substitute into the second:
#s_p-25=(4(s_p+25))/5#
#5s_p-125=4s_p+100#
#s_p=225mph#