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### 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

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/
```
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