An airplane made a trip of 815 miles in 4 hours. part of the trip was made at 180 miles per hour and the remainder at 220 miles per hour. find the number of miles traveled at the slower rate.

We have 2 situation one with wind and one against wind

Speed = x , W= Wind

*case 1       ( With Wind)                     *case 2      ( Against Wind)

t=3 hr  d= 2160 m.  Rate = x + W            t=4 hr  d= 2160 m.  Rate = x - W

Distance = Rate * Time

2160 =  (x+W) * 3                                                      2160 = (x-W) * 4

2160 / 3 = (x+W)                                                        2160/4 = x-W

720 = x+W                                                                  540 = x-W

NOW 2 equations solve by substitution or elimination.  ( i did Elimination)

720 = x+W

540 = x-W

1260 = 2x    (W was eliminated) solve for x

x = 630  Speed of the Airplane 

now solve for W. W = 90  Speed of the Wind

 hope this helps

b) 1/3 * 1/5

step-by-step explanation:

each smallest part is 1/15 since the written one is 1/5 and it's divided by 3 equal parts. (1/5 )/3 = 1/15 = 1/3 * 1/5

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have