GB-17-03-001 · Inverse proportion in context

14 identical machines complete a job in 5 hours.

(a) Work out how long 4 of these machines would take.

(b) State one assumption used in your calculation.

Part (a) Machine Days (Inverse Proportion) Booklet p. 24

Method

1) Total machine-hours = Machines × Hours

2) Divide total machine-hours by the new number of machines

Worked Example (GB-17-03-001 · Part (a))

Work out how long 4 of these machines would take.

Booklet p. 24 — Machine Days (Inverse Proportion):

1) Total machine-hours

= \text{Machines} \times \text{Hours} = 14 \times 5 = \mathbf{70}

2) For

4

machines:

70 = 4 \times T \;\Rightarrow\; T = \frac{70}{4}

\frac{35}{2}

hours

More machines

\Rightarrow

less time (multiply

M \times H

for total work!)

Part (b) Machine Days (Inverse Proportion) Booklet p. 24

Method

State an assumption needed for the proportional model

Worked Example (GB-17-03-001 · Part (b))

State one assumption used in your calculation.

The machines all work at the same constant rate, with no delays.

The inverse relationship assumes the same amount of work and the same constant rate per machine.

Ans = The machines all work at the same constant rate, with no delays.