Two People are Faster than One

Date: 4/17/96 at 16:59:44
From: "AIREY_DENNIS"
Subject: Please Help!

     Math Swat Team,

     Please help me solve this problem:

     It takes Mary 100 hours longer than Ken to drink a case of
     beer.  If it takes 2 hours to drink the case together, how
     long would it take Mary to drink the case alone?

     My friend James O. Kent, Esq. gave me this problem.

     Thanx.

     Dennis Airey

Date: 5/3/96 at 15:4:45
From: Doctor Steven
Subject: Re: Please Help!!

Denote Ken's rate of drinking by Rk and Mary's rate of drinking 
by Rm.

Then Rk = 1 case/x hours  and Rm = 1 case/(x + 100) hours.

Now 1 case/2 hours = Rk + Rm.

So 1/2 = 1/x + 1/(x + 100)

Multiply by 2 on both sides and get:

 1 = 2/x + 2/(x + 100).

Multiply by x on both sides and get:

 x = 2 + 2x/(x + 100)

Multiply by (x + 100) on both sides and get:

 x^2 + 100x = 2x + 200 + 2x.

So we get:

 x^2 + 96x - 200 = 0.

Use the quadratic equation to find x:

 x = [-96 + Sqrt(96^2 + 800)]/2 = -48 + Sqrt(10016)/2

   = -48 + 2*Sqrt(626) (almost)= 2.04.

So Ken's rate of drinking is 1 case/2.04 hours!
That's about 11.75 beers an hour, one beer every 5.5 minutes!

Mary on the other hand drinks a case of beer in 102.04 hours 
or 4 days: this means she drinks on average about 5.5 cans 
of beer a day.

Of that case Ken drank 23.5 beers and Mary had .5 beers.

Wow.

-Doctor Steven,  The Math Forum