Plane Flying with a Tailwind

Date: 9/8/96 at 20:48:56
From: Anonymous
Subject: Plane Flying with a Tailwind

A jet is flying 2400 miles from Hawaii to San Francisco.  In still 
air, it flies at 600 mph. There is a 40 mph tailwind.  How many hours 
after takeoff would it be faster to just go to San Francisco than to 
return to Hawaii in the case of an emergency?

I need the formula to solve this problem.  My teacher told us the 
answer is 1.75 hours.  I tried dividing 640mph into 1200 (midpoint of 
travel) and got 1.875 hours.  Then I thought that if one was to turn 
around after flying 1.75 hours, that it would take longer to get back 
to Hawaii because the speed would be 560 mph.  I can't visualize this 
- can you help me?

Thanks!

Date: 9/9/96 at 11:49:23
From: Doctor Robert
Subject: Re: Plane Flying with a Tailwind

Flying TO San Francisco, the plane's speed is 640 mph.  If it were 
flying back to Hawaii, its speed would be 560 mph.

Let t be the number of hours of flight.  Then it has flown a distance 
of 640t miles and the distance yet to go is 2400 - 640t.  The time 
left to fly is then (2400-640t)/640.  However, if it were to return to 
Hawaii, it would have to fly 640t miles at 560 mph which would then 
take 640t/560 hrs. If we equate these times we have

   (2400-640t)/640 = 640t/560

If you solve this equation for t you get t = 1.75 hr.  

-Doctor Robert,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/