Joe flies a plane 300 miles in 2 hours to a destination with the wind. On the return trip against the wind, he only flies 270 miles in 2 hours. Assuming wind speed is constant, what's the wind speed?

2 Answers

Answer:

Airplane = 142.5 mph. Wind = 7.5 mph.

Explanation:

Let's think of the problem this way:

On the first leg of the trip , Joe flew 300 miles in 2 hours. We can then say that he flew:

#(300 " miles")/(2 " hours")=150 mph#

Since this was in the same direction of the wind, the plane was going the speed of the plane in still air plus the speed of the wind:

#"Airplane speed " + " wind speed" = 150 mph#

On the return trip, Joe flew 270 miles in the same 2 hours. We can say that he flew:

#(270 " miles")/(2 " hours")=135 mph#

Since this was in the opposite direction of the wind, the plane was going the speed of the plane in still air minus the speed of the wind:

#"Airplane speed " - " wind speed" = 135 mph#

Putting it together

We can add the two equations:

#"Airplane speed " + " wind speed" = 150 mph#
#ul("Airplane speed " - " wind speed" = 135 mph#
#2xx"Airplane speed"=285mph#

Which means that #"Airplane speed" =285/2=142.5mph#

The wind speed is then: #142.5+"wind speed"=150=>"wind speed"=7.5mph#

Apr 14, 2017

Answer:

Wind speed: #w=7.5mph#

Speed of plane in still air: #142.5mph#

Explanation:

Flying with the wind Joe flew #300m# in #2h#
Flying against the wind Joe flew #270m# in #2h#

Then we can equate his relative speeds (in still air) there and back to his present location, since the times are the same. We will use #w# for the wind speed:

Outbound, Joe's air speed (no wind) is: #(300mph)/(2h)-w#

The wind has to be subtracted because here it is adding to the speed of the plane in still air.

Inbound, Joe's air speed (no wind) is: #(270mph)/(2h)+w#

The wind has to be added because here it is reducing the speed of the plane in still air.

Then: #(300)/(2)-w=(270)/(2)+w#

#(300)/(2)-(270)/(2)=w+w#

#300-270=2(w+w)#

#30=4w#

#w=7.5mph# which is the wind speed

Outbound, Joe's air speed (no wind) is: #(300mph)/(2h)-w#

#300/2-7.5=142.5mph#

Inbound, Joe's air speed (no wind) is: #(270mph)/(2h)+w#

#270/2+7.5=142.5mph#