Four mechanics at a car workshop, all working at the same steady rate, can service a whole fleet of delivery vans in 9 hours. The workshop manager wants the...
Question 1 Report
Four mechanics at a car workshop, all working at the same steady rate, can service a whole fleet of delivery vans in 9 hours. The workshop manager wants the fleet ready sooner for a busy bank holiday weekend.
- Find how long 6 mechanics would take to service the same fleet. (2)
- Find the least number of mechanics needed to finish the service within 4 hours. (2)
Answer Details
This question tests inverse proportion between the number of mechanics and the time taken to service a fixed fleet of vans.
- With 4 mechanics the constant is \(4 \times 9 = 36\) mechanic-hours. With 6 mechanics, the time is \(36 \div 6 = \) 6 hours [2].
- To finish within 4 hours, mechanics \(\geq 36 \div 4 = 9\). The least number of mechanics needed is 9 [2].
The 36 mechanic-hours is the fixed total workload of servicing the fleet; more mechanics working together share that same fixed workload in less time, which is the defining feature of inverse proportion.
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