Four diggers, two ditches, six hours, now three diggers, five ditches

Question

Four people dig two ditches in 6 hours. Solve in your head. How long do three people take to dig five ditches? Aim: under 20 seconds.

Accepted Answer

Work in person-hours, but first find the cost of a single ditch, the given rate already covers two: - Two ditches cost 4 	imes 6 = 24 person-hours, so one ditch costs 24 / 2 = 12 person-hours. - Five ditches cost 5 	imes 12 = 60 person-hours. - Three people supply 3 person-hours per hour, so \frac{60}{3} = 20 	ext{ hours}. Takeaway. When the stated job is a multiple, normalize to one unit first (cost per ditch), then scale. Reducing to the per-job cost before scaling keeps the arithmetic in whole numbers and avoids mixing up the two ratios.

Four diggers, two ditches, six hours, now three diggers, five ditches

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