Question

Against the wind a small plane flew 210 miles in 1 hour and 10 minutes. The return trip took only 50 minutes. How do you determine the speed of the plane?

Answer 1

Speed of the plane `=3.6` miles/minute `=216` miles/hour

Explanation:

If `s_p` is the speed of the plane (in miles per minute)
and `s_w` is the speed of the wind (in miles per minute)

We are told
[1]`color(white)("XXX")s_p-s_w=210/70`
[2]`color(white)("XXX")s_p+s_w=210/50`

Adding [1] and [2]
[3]`color(white)("XXX")2s_p = (21cancel(0))/(7cancel(0))+(21cancel(0))/(5cancel(0))`

[4]`color(white)("XXX")2s_p = (105+147)/35`

[5]`color(white)("XXX")2s_p= 252/35`

[6]`color(white)("XXX")s_p = 126/35 = 18/5 = 3.6`

`3.6` miles/ minute
`color(white)("XXX")= 3.6 ("miles")/(cancel("minute"))*60 (cancel("minutes"))/("hour") = 216 ("miles")/("hour")`

Answer 2

I found `3.6("miles")/min`

Explanation:

Call `v_p` the plane velocity and `v_w` the wind velocity.
Against the wind you have:
`v_p-v_w=210/70`
where I used the fact that velocity=distance/time and changed time in minutes.
When the wind is in the same direction you get:
`v_p+v_w=210/50`

From the first equation:
`v_p=v_w+210/70=v_w+3` substitute into the second:
`v_w+3+v_w=4.2`
`2v_w=1.2`
`v_w=1.2/2=0.6("miles")/min`
and using this into: `v_p=v_w+3`
`v_p=3.6("miles")/min`