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?

2 Answers
Oct 3, 2015

Answer:

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")#

Oct 3, 2015

Answer:

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#