Find the rate of the wind

Question

An airplane travels 1,800 miles from Los Angeles to Chicago in 3.6 hours, going with the wind. The return trip takes 4 hours and is against the wind. Find the rate of the airplane with no wind. Find the rate of the wind.

Answer 1

This is the velocity type of a word problem. You can also encounter it in the form of a boat traveling with or against the river current. The solutions use formula velocity = distance / time, v = d / t.

Let v_a be rate (velocity) of the airplane with no wind

Let v_w be rate (velocity) of the wind

With the wind, velocity is v_a+w = v_a + v_w = d_a+w / t_a+w = 1800 / 3.6 = 500

Against the wind, velocity is v_a-w = v_a - v_w = d_a-w / t_a-w = 1800 / 4 = 450

Adding together the two boldfaced equations 2v_a = 950

v_a = 950 / 2 = 475 km/h

v_w = v_a+w - v_a = 500 - 475 = 25 km/h

Answer: Rate of the airplane with no wind is 475 km/h. Rate of the wind is 25 km/h

Answer 2

1800/3.6 = 500 mph

1800/4 = 450 mph

 

The plane is aided by the wind there and hampered on the way back.

 

a + w = 500

a - w = 450

 

Adding the two together...

 

2a = 950

a = 475

 

I bet you can find w!