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Difficulty: MediumDirect Proportions

An automated wire-cutting machine processes 350350 meters of copper wiring in 2020 minutes. Operating at this constant rate, how many meters of wiring will the machine process in 1.51.5 hours?

Answer: 1575 meters

Answer

1575
Because the machine operates at a constant rate, the relationship between time and wire processed is directly proportional. However, the time units differ between the given rate (2020 minutes) and the target time (1.51.5 hours). First, convert 1.51.5 hours to 9090 minutes. Then, set up the direct proportion 350 meters20 minutes=x meters90 minutes\frac{350 \text{ meters}}{20 \text{ minutes}} = \frac{x \text{ meters}}{90 \text{ minutes}}. Solving for xx by multiplying 350350 by 9090 and dividing by 2020 yields exactly 15751575 meters.

Step-by-Step Solution

1
Harmonize the time units by converting hours to minutes.
9090 minutes
The given rate is in meters per minute, so the target time must also be in minutes to establish a valid equivalent ratio.
2
Set up a direct proportion equation.
35020=x90\frac{350}{20} = \frac{x}{90}
The length of wire processed increases at a constant, directly proportional rate to the time operated.
3
Solve the proportion for the unknown value xx.
x=1575x = 1575
Cross-multiplying and simplifying isolates xx, calculating the total meters processed in the longer timeframe.

Key Concept

Direct proportions with unit harmonization
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Topics

Direct Proportions

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