Math problem!!?

Question

A plane on a search mission flew east from an airport, turned and flew west back to the airport. The plane cruised at 200km/h when flying east and 300km/h when flying west. If the plane was in the air for 6 hours, how far from the airport did it travel?

Answer 1

Draw it as a diagram - that might help. possibly.

Answer 2

Assuming instantaneous speed from the moment of takeoff to the moment of landing, and no loss during the turnaround (which you have to do for these problems), the two distances must be equal. Let t be the time at 300 km/h, and 6-t be the time at 200 km/h. So 300t = 200(6-t). (Distance = rate times time)

300t = 1200-200t. Add 200t to both sides, 500t = 1200. Divide both sides by 500, and t = 12/5 hours, or 2.4 hours. To get the distance traveled, multiply 300 by 2.4.

Answer 3

Jayjay,

The answer depends on the winds encountered by the plane as it travels. Assuming no wind at all, the plane would travel for 3.6 hours to the east at 200km/hr for a total of 720km. Its return trip would take 2.4 hours to the west at 300km/hr for a total of 720km.

With a wind from the west at 20km/hr a plane traveling through the air at 200km/hr would fly across the ground going east at 220km/hr. This is because the air is moving towards the east at 20km/hr, but the plane's spedometer only shows how fast you are moving through the air, not how fast you are moving across the ground (unless you have the proper equipment to show you how fast you are going across the ground like a GPS system or a DME-distance measuring equipment). For this wind the eastbound leg of the trip would take 3.36 hours at 220km/hr for 739.2km travelled. The westbound leg would take 2.64 hours at 280km/hr for 739.2km. Remember the spedometer on the airplane would be telling you that you were travelling eastbound at 200km/hr and westbound at 300km/hr, but with the wind your speed across the ground would be 220km/hr east and 280 west. This is for simple measurements because as you fly higher there are also speed differences through the air as compared to the speed over the ground simply because the air gets thinner as you go higher.

So depending on the winds the answer would change. Another example would be if the wind were from the west at 50km/hr. The plane would move through the air eastbound at at 200km/hr but across the ground at 250km/hr. It would travel for 3 hours for a total of 750km. The westbound leg would move through the air at 300km/hr but only be travelling across the ground at 250km/hr for the remaining 3 hours and for a total of 750km.