How do I know what ratio I need to invert in an inverse compound rule of three problem?

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Example: Alejandro's father hired 15 workers who, working 40 days for 10 hours a day, built a swimming pool in his house with a capacity for 80,000 liters of water; If Alejandro hires 10 of these workers to work 6 hours a day and build another pool with a capacity of 40,000 liters of water, how many days will it take him to build it?

Workers: 15 // 10

Hours: 400 // x

Liters: 80 000 // 40 000

  1. (15/10)(2) = x/400

x = 12000 -> 1200/6 = 200 days

  1. (10/15)(2) = 400/x

x = 300 -> 300/6 = 50 days

The second equation is the correct one.

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You have $15$ workers working for $400$ hours to create $80000$ liters of capacity. That means $6000$ worker-hours are necessary to create $80000$ liters of capacity.

Now you want to create $40000$ liters of capacity. That obviously will require $3000$ worker-hours. You have $10$ workers working $6$ hours per day, so you're getting $60$ worker-hours per day. That means that in $\frac{3000}{60}=50$ days, you'll have accumulated the $3000$ worker-hours you needed.

I find it easier to understand what's going on in the real world than to memorize formulae.