Answer:
Plane = 441 mi/h; wind = 63 mi/h
Step-by-step explanation:
distance = rate × time
Let p = the plane's speed in still air
and w = the wind speed . Then,
p + w = speed with wind
p - w = speed against wind
We have two conditions:
(1) 756 = (p - w) × 2
(2) 756 = (p + w) × 1.5
Distribute the constants (3) 756 = 2p - 2w
(4) 756 = 1.5p + 1.5 w
Multiply Equation (3) by 3 (5) 2268 = 6p - 6w
Multiply Equation (4) by 4 (6) 3024 = 6p + 6w
Add Equations (5) and (6) 5292 = 12p
Divide each side by 12 (7) p = 441 mi/h
Substitute (7) into Equation(3) 756 = 882 - 2w
Add 2w to each side 2w + 756 = 882
Subtract 756 from each side 2w = 126
Divide each side by 2 w = 63 mph
The plane's speed in still air is 441 mi/h.
The wind speed is 63 mph.
Check:
(1) 756 = (441 - 63) × 2 (2) 756 = (441 + 63) × 1.5
756 = 378 × 2 756 = 504 × 1.5
756 = 756 756 = 756
