What is the wind speed?

Question

A flight from Seattle to New York, with a tailwind, takes 5 hrs 15 min, and the return flight take 6 hrs 35 minutes. Since the flight time includes time to taxi from and to the gate, we should subtract 45 minutes from each time to account for this. Not shown, I was able to find out the plane was scheduled to fly a 2481 mile flight path. Assuming the plane and wind speeds are constant during both flights, estimate the wind speed, to 1 decimal place.

Answer 1

with tailwind 5 hrs 15 min -45 min = 4 hrs 30 min

against the wind 6 hrs 35 min = 5 hrs 50 min

distance = 2,481 miles = d = rt

w + p = r = rate of speed with wind

p-w = r = rate of speed against wind

d = same both ways

set them equal

w + p)(4 1/2) = 2481 = (p-w)(5 5/6)

multiply by 6

27w +27p = 6(2481) = 35p -35w

35p -35w = 6(2481)

27w +27p = 6(2481

27(35p) -27(35w) = 27(6(2481)

35(27w) +35(27p) = 35(6(2481)

add to eliminate w

2(27)(35)p = 35(6(2481)

divide by 35(6)

9p = 2481

p = 2481/9 = 827/3 =275 2/3 mph = about 275.33 mph = plane's speed in still air

27w +27p = 6(2481)

9w +9p =2(2481)

w = (2(2481 - 9p)/9 = 2(2481)/9 - p = 2(827)/3 - 275.33 = 1654/3 -275.33 = 551.33 -275.33 = 276 mph

w = wind speed= 276 mph

exactly, not rounded