Answer:
plane speed = 520 mph
wind speed = 20 mph
Step-by-step explanation:
let the speed of the wind be w mph and the speed of the plane be p mph
flying from NY to NM,
time taken = 3 hr 36 min = 3.6 hr
average ground speed = total distance / time taken
= 1800 / 3.6 = 500 mph
since it is a headwind, the plane speed will be slowed down by the head wind, resulting in a lower ground speed.
we can write the following equation:
ground speed = plane speed - wind speed
500 = p - w ------(eq1)
flying from NY to NM (return flight),
time taken = 3 hr 20 min = 3.333 hr
average ground speed = total distance / time taken
= 1800 / 3.333 = 540 mph
on the return trip, the headwind becomes a tailwind, hence the total ground speed would be faster than the plane's air speed , we can write the following equation:
ground speed = plane speed + wind speed
540 = p + w ------(eq2)
with these 2 systems of equations, we can solve for p & w using either substitution of elimination method.
eventually you will end up with
plane speed = 520 mph
wind speed = 20 mph
