Question 1197406
SETTING UP AND SOLVING DIRECT AND INVERSE PROPORTIONS
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.
<pre>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,
and vice-versa. However, your setup is WRONG!

With P being the number of pumps, k being the CONSTANT of PROPORTIONALITY,  and T, the amount of time,
we get: {{{matrix(1,3, P, "=", k/T)}}}
        {{{matrix(1,3, 2, "=", k/(5&1/2))}}} ---- Substituting 2 for P, and T for amount of time taken by both pumps
        {{{matrix(1,5, k, "=", 2(5&1/2), "=", 11)}}} ---- Cross-multiplying

With 3 pumps (P) working at the same rate, k, or CONSTANT of PROPORTIONALITY being 11, and T being 
amount of time the 3 pumps will take to drain it out, we get: {{{matrix(1,7, P, "=", k/T, "=====", 3, "=", 11/T)}}}
                                                                           3T = 11 ------ Cross-multiplying
                           Time it'll take the 3 pumps to drain it out, or {{{highlight_green(matrix(1,11, T, "=", 11/3, or, 3&2/3, "hours,", or, 3, "hours,", 40, minutes)))}}}</pre>