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Two People are Faster than One

Date: 4/17/96 at 16:59:44
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.


     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.


-Doctor Steven,  The Math Forum

Associated Topics:
Middle School Word Problems

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