If one cat eats 1.5 rats in 1.5 days, then in how many days will 3 cats eat 3…

Concept

Work-rate problems like this rest on one idea: if every worker (here, each cat) eats at a constant, identical rate, a group's combined eating rate is the individual rate multiplied by the number of workers, and the time to finish a job equals the amount of work divided by the combined rate.

Applying it here

1. Find one cat's rate: 1 cat eats 1.5 rats in 1.5 days, so its rate = 1.5 rats ÷ 1.5 days = 1 rat per day.

2. Scale to the group: 3 cats eating at the same rate together consume 3 × 1 = 3 rats per day.

3. Find the time: eating 3 rats at a combined rate of 3 rats per day takes 3 ÷ 3 = 1 day.

Cross-check

Scale the given ratio directly instead: doubling both rats and days (1.5 rats in 1.5 days) shows 1 cat would eat 3 rats in 3 days. Tripling the number of cats to 3 divides that time by 3, since three cats finish the same 3 rats three times as fast, giving 3 ÷ 3 = 1 day — the same result.

Answer

3 cats eating 3 rats at this rate takes 1 day.