My question follows the following:
A swimming pool fills at a rate of 400 gallons every 60 minutes. How long will it take to fill it with 3,600 gallons?
Solution: 60/? = 400/3,600
? = 540
From the above, 60 minutes is to ? minutes as 400 gallons is to 3,600 gallons.
What does the above mean, that is, how are 60 minutes to ? minutes as 400 gallons are to 3,600 gallons?
I know that 540 divided by 60 is 9 and 1/9 of 540 is 60 and likewise 3,600 divided by 400 is 9 and 1/9 of 3,600 is 400, but is this what the above indicates or is there more?
I thank you for your reply.
You can compare gallons to gallons and set them equal to minutes to minutes or you can compare gallons per minutes to gallons per minutes which is the usual way to perceive the proportion. If it takes 60 minutes for every 400 gallons then it takes x minutes to put in 3600 gallons which is to say 60/400 = x/3600 (Note: you can reduce a ratio so in this case you have 6/40 = x/3600, which makes the math without a calculator easier). Multiply both sides by 3600 getting x = 6*3600/40 = 6*360/4 (since there is a zero in both 3600 and 40) = 6*90 (since 360/4 is 90) = 5400 as you already ascertained. Ratios are just a comparsion of two numbers and when two ratios are equal you have a proportion.
I hope this suffciently answers your questions?