Question 1171013

a plane traveled "2835" miles with the wind in 4.5 hours and "2475" miles against the wind in the same amount of time. find the speed of the wind.
<pre>Let speeds, of plane in still air, and wind, be S and W, respectively
We then get: {{{system(matrix(2,3, S + W, "=", "2,835"/4.5, S + W, "=", 630), matrix(1,6, S, "=", 630 - W, "----", eq, "(i)"))}}}
       Also, {{{system(matrix(1,3, S - W, "=", "2,475"/4.5), matrix(1,6, S - W, "=", 550, "-----", eq, "(ii)"))}}}
630 - W - W = 550 ------ Substituting 630 - W for S in eq (ii)
       - 2W = 550 - 630
       - 2W = - 80
Wind speed, or {{{highlight_green(matrix(1,6, W, "=", (- 80)/(- 2), "=", 40, mph))}}}