Question 204385
Using {{{d = rt}}} where d = distance traveled, r = rate/speed, and t = time of travel.
For the outbound trip: {{{d[1] = 1815}}} miles, {{{r[1] = (525+w)}}}mph.
For the return trip: {{{d[2] = 1335}}} miles, {{{r[2] = 525-w)}}}mph.
So we can set up the two equations: (w = wind speed)
1) {{{1815 = (525+w)*t}}}
2) {{{1335 = (525-w)*t}}} The time, t, is the same for both trips. Solve both equations fo t and set them equal to each other.
1) {{{t = 1815/(525+w)}}}
2) {{{t = 1335/(525-w)}}} so...
{{{1815/(525+w) = 1335/(525-w)}}} Now we solve for w, the speed of the wind. Cross-multiply.
{{{1815(525-w) = 1335(525+w)}}}
{{{952875-1815w = 700875+1335w}}} Subtract 700875 from both sides.
{{{252000-1815w = 1335w}}} Add 1815w to both sides.
{{{252000 = 3150w}}} Finally, divide both sides by 3150.
{{{highlight(w = 80)}}}mph.