A small plane flying into a wind takes 3h to travel 780 km from Lethbridge to Ft. McMurray. At the same time, a similar plane leaves Ft. McMurray and arrives at Lethbridge in 2.5h. If the planes have the same cruising speed in windless conditions, determine the speed of the wind.
2007-07-04 12:24:35 · 3 answers · asked by Lucy X 2 in Science & Mathematics ➔ Mathematics
780km/3h = 260 km/hr
780km/2.5h = 312 km/hr
One of these is the plane speed plus wind speed, the other the plane speed minus wind speed:
p + w = 312
p - w = 260
Subtract the second from the first to cancel p:
p - p + w - (-w) = 312 - 260
2w = 52
w = 26
The wind speed is 26 km/hr.
2007-07-04 12:32:53 · answer #1 · answered by McFate 7 · 0⤊ 0⤋
Both planes are making the same speed thru the air, but a different speed over the ground due to the wind.
Let A be the speed of the planes thru the air, let B be the wind speed.
Plane 1' speed over ground = 780km/3 hrs = A-B (air spd - wind spd)
Plane 2 speed over ground = 780 km/2.5 hrs= A+B (air spd + wind spd)
so, 260 = A - B
and 312 = A + B
add the 2 equations
572 = 2 A
A = 286 km/hr
substitute into either of the 2 equations:
260 = 286 - B
B = 26 km/hr
check
312 = 286 + 26
done
2007-07-04 19:35:30 · answer #2 · answered by Scott W 3 · 0⤊ 0⤋
780/3 = 260
780/2.5 =312
312 - 260 = 52
52 / 2 = 26 km/hr
2007-07-04 19:47:13 · answer #3 · answered by Anonymous · 0⤊ 0⤋