View Full Version : Need help with algebra word problem (headwind/tailwind)

07-14-2011, 02:01 AM
Hi there! My name is Olga, and this is my first time using a resource like this, so here goes:

The question I have to solve is as follows:

"Flying to Kampala with a tailwind a plane averaged 158 km/h. On the return trip the plane only
averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of
the plane in still air."

I have figured out the following, but don't know where to go next since I don't have a time or distance to work with:

P (plane speed)
W (wind speed)

P + W = 158 mph
P - W = 112 mph

I tried using 1hr as the time, but then all I get is 158 = 112, which makes no sense. I also tried combining the speeds and making an equation such as 170 = (p+w) (p-w), but I don't think that's right, and I don't remember how to factor either...it's been a long time since I've done algebra...preping for the GMAT now and I need all the help I can get...

thanks guy/gal volunteers working on this site!!


07-14-2011, 07:53 AM
Try adding and subtracting your equations.

07-14-2011, 10:51 AM
This is just a system of two linear equations in two unknowns. You do not need to know time and distance.

There are numerous methods for solving a system of n linear equations in n unknowns.

In the case of your problem, the simplest technique is to add the two equations together as royhaas has already explained.

Try looking at http://www.themathpage.com/alg/simultan ... ations.htm (http://www.themathpage.com/alg/simultaneous-equations.htm) (with a short discussion of which methods are most useful at viewtopic.php?f=9&t=47595 (http://www.freemathhelp.com/forum/viewtopic.php?f=9&t=47595)).

07-14-2011, 12:14 PM
Ooooooh....!! Haha, thanks! Funny thing is, after I posted this I went on to solve 5 more ticket sales problems where I used the addition of the equations to solve them...I don't know why I got confused with that one...

Anyway, thanks for the help...I'm really excited to be a part of this community!