Question

Lap pool A lanes for 3 swimmers and lap pool has lanes for 10 swimmers. The lap pools have the same uniform depth. Lap pool B contains approximately 6.6x10^5 gallons of water. Estimate the number of gallons of water in lap pool A

Answer 1

Answer:

approximately 2x10^5 gallons of water

Step-by-step explanation:

It is given that both pools have equal depths and if we assume that their lengths are also same (lanes are the same length) then the only difference between the pools is their widths (3 lanes vs. 10 lanes).

If we mark width of one lane with W, length with L and depth with D we'll get that the volume of each lane is W•L•D. This is the volume expressed in cubic feet, so if we want it in gallons we multiply that with 7.5.

Now, pool A has 3 lanes, so its volume is 3 times volume of one lane:

Va (in gallons) = 3•W•L•D•7.5

Pool B has 10 lanes, so its volume is 10 times volume of one lane:

Vb (in gallons) = 10•W•L•D•7.5

So, Va:Vb is 3•W•L•D•7.5 : 10•W•L•D•7.5

When we cancel out the same values, we are left with:

Va : Vb = 3 : 10

It is given that Vb is 6.6x10^5:

Va : 6.6x10^5 = 3 : 10

Va = (3•6.6x10^5)/10

Va = 2x10^5 gallons