A factory uses 8 identical machines to produce 480 items in 6 hours. If 3 of the machines … — JAMB UTME

A factory uses $8$ identical machines to produce $480$ items in $6$ hours. If $3$ of the machines break down, how many hours will it take the remaining machines to produce $600$ items at the same rate?

Answer: 12 hours

Answer

The remaining machines will take 12 hours to produce 600 items.

Each machine produces

\frac{480}{8 \times 6} = 10

items per hour. With

5

active machines, the combined rate is

50

items per hour. To reach

600

items, the time required is

\frac{600}{50} = 12

hours.

Step-by-Step Solution

Calculate the output rate per machine per hour

10 items per machine per hour

The combined rate of 8 machines is

480 \div 6 = 80

items per hour. Dividing by 8 machines gives

10

items/hour per machine.

Determine the new combined production rate

50 items per hour

With 3 machines out of service,

8 - 3 = 5

machines remain, working at a total rate of

5 \times 10 = 50

items per hour.

Calculate total hours required for the new target quantity

12 hours

Dividing the target quantity of

600

items by the rate of

50

items/hour yields

\frac{600}{50} = 12

hours.

Key Concept

Compound Proportion and Work Rate

Estimated Time:1m 30s

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