Machine A produces 120 widgets in 4 hours at a constant rate, and Machine B produces 150 w… — GMAT

Machine A produces $120$ widgets in $4$ hours at a constant rate, and Machine B produces $150$ widgets in $3$ hours at a constant rate. If both machines work simultaneously at their respective constant rates, how many total widgets will they produce in $2$ hours?

Answer: 160 widgets

Answer

The total number of widgets produced by both machines in 2 hours is 160.

Machine A produces

30

widgets per hour (

120 \div 4

), and Machine B produces

50

widgets per hour (

150 \div 3

). Together, their combined rate is

80

widgets per hour (

30 + 50

). Working together for

2

hours, they produce a total of

160

widgets (

80 \times 2

Step-by-Step Solution

Find the hourly rate of Machine A

Machine A produces

\frac{120}{4} = 30

widgets per hour.

Dividing total output by time gives the unit work rate per hour.

Find the hourly rate of Machine B

Machine B produces

\frac{150}{3} = 50

widgets per hour.

Dividing total output by time gives the unit work rate per hour.

Calculate the combined production rate per hour

The combined rate is

30 + 50 = 80

widgets per hour.

When working simultaneously, individual rates add together.

Multiply combined rate by the target time

2

hours, total production is

80 \times 2 = 160

widgets.

Total work equals rate multiplied by time.

Key Concept

Combined Work Rates

Estimated Time:45s

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