document.write( "Question 1197406: SETTING UP AND SOLVING DIRECT AND INVERSE PROPORTIONS
\n" ); document.write( "Two sump pumps working at the same rate to drain a flooded basement in 5 1/2 hours. How long would it have taken 3 pumps working at the same rate to drain the basement? I think it is an inverse proportion and I put 2 over 3 = 5 1/2 over x multiplied and got 2x=16 1/2 divided and got 8 1/4. But it is supposed to take less time not more. \n" ); document.write( "

Algebra.Com's Answer #830950 by MathTherapy(10555) $\"\"$ $\"About$

You can put this solution on YOUR website!
SETTING UP AND SOLVING DIRECT AND INVERSE PROPORTIONS
\n" ); document.write( "Two sump pumps working at the same rate to drain a flooded basement in 5 1/2 hours. How long would it have taken 3 pumps working at the same rate to drain the basement? I think it is an inverse proportion and I put 2 over 3 = 5 1/2 over x multiplied and got 2x=16 1/2 divided and got 8 1/4. But it is supposed to take less time not more.
\n" ); document.write( "

You're correct in that it's INVERSE VARIATION, because the more pumps are used, the less time it'll take it/them to do the job,\r\n" );
document.write( "and vice-versa. However, your setup is WRONG!\r\n" );
document.write( "\r\n" );
document.write( "With P being the number of pumps, k being the CONSTANT of PROPORTIONALITY,  and T, the amount of time,\r\n" );
document.write( "we get: \r\n" );
document.write( "         ---- Substituting 2 for P, and T for amount of time taken by both pumps\r\n" );
document.write( "         ---- Cross-multiplying\r\n" );
document.write( "\r\n" );
document.write( "With 3 pumps (P) working at the same rate, k, or CONSTANT of PROPORTIONALITY being 11, and T being \r\n" );
document.write( "amount of time the 3 pumps will take to drain it out, we get: \r\n" );
document.write( "                                                                           3T = 11 ------ Cross-multiplying\r\n" );
document.write( "                           Time it'll take the 3 pumps to drain it out, or

\n" ); document.write( "

\n" );