Eight machines, twelve hours, now six machines, two jobs

Question

Eight identical machines complete one job in 12 hours. Solve in your head. How long do six machines take to complete two jobs? Aim: under 15 seconds.

Accepted Answer

Convert everything to machine-hours, the invariant unit of work: - One job costs 8 	imes 12 = 96 machine-hours. - Two jobs cost 192 machine-hours. - Six machines supply 6 machine-hours per hour, so \frac{192}{6} = 32 	ext{ hours}. Takeaway. Rate problems collapse when you name the conserved quantity (machine-hours, worker-days, tank-litres) and do two clean divisions. Skipping the "rate per machine" step avoids fractions entirely. The classic trap, scaling time down when machines decrease, can't happen if you route through total work.

Eight machines, twelve hours, now six machines, two jobs

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