Question

Emptying Oil Tankers An oil tanker can be emptied by the main pump in 4 hours. An auxiliary pump can empty the tanker in 9 hours. If the main pump is started at $9 \mathrm{AM},$ when should the auxiliary pump be started so that the tanker is emptied by noon?

Name: Problem 49, Chapter 1: College Algebra
Uploaded: 2023-04-21T04:44:49-08:00
Duration: 4 min 3 s
Channel: Aman Gupta
Description: Emptying Oil Tankers An oil tanker can be emptied by the main pump in 4 hours. An auxiliary pump can empty the tanker in 9 hours. If the main pump is started at 9 AM, when should the auxiliary pump be started so that the tanker is emptied by noon?

   Emptying Oil Tankers An oil tanker can be emptied by the main pump in 4 hours. An auxiliary pump can empty the tanker in 9 hours. If the main pump is started at $9 \mathrm{AM},$ when should the auxiliary pump be started so that the tanker is emptied by noon?

College Algebra

Michael Sullivan 11th Edition

Chapter 1, Problem 49

Instant Answer

Solved by Expert Aman Gupta

04/21/2023

Step 1

The rate at which the main oil tanker works is $\frac{w}{4}$ work per hour and the rate at which the auxiliary oil tanker works is $\frac{w}{9}$ work per hour. Show more…

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Emptying Oil Tankers An oil tanker can be emptied by the main pump in 4 hours. An auxiliary pump can empty the tanker in 9 hours. If the main pump is started at $9 \mathrm{AM},$ when should the auxiliary pump be started so that the tanker is emptied by noon?

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Key Concepts

Work Rate

A work rate is the amount of work done per unit of time. In problems like this, each pump has a work rate calculated by taking the reciprocal of the time it takes to complete the job individually. This concept is essential for setting up equations that model work done over time.

Combined Work Rate

When multiple agents (in this case, pumps) work together either simultaneously or in overlapping time intervals, their work rates add up. Understanding how to combine these rates is crucial for determining the total work done and for planning the sequence of operations to meet a deadline.

Time Management in Work Problems

This concept involves partitioning the total available time into segments during which different agents work. By precisely scheduling start times and durations, one ensures that the aggregated contribution meets the total work requirement by the target completion time. This skill is vital in many real-world planning scenarios.

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