Precalculus Enhanced with Graphing Utilities
Precalculus Enhanced with Graphing Utilities
6th Edition
ISBN: 9780321795465
Author: Michael Sullivan, Michael III Sullivan
Publisher: PEARSON
Question
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Chapter A.8, Problem 47AYU
To determine

To find: When should the auxiliary pump be started so that the tanker is emptied by noon?

Expert Solution & Answer
Check Mark

Answer to Problem 47AYU

Started the auxiliary pump at 9:45 AM.

Explanation of Solution

Given:

An oil tanker can be emptied by the pump in 4 hours. An auxiliary pump can empty the tanker in 9 hours. If the main pump is started at 9 am.

Calculation:

The main pump’s emptying rate is 1 4 tanker per hour. It will be open the entire 3 hours, so it will empty 3 4 of the tank.

The other 1 4 of tank must be emptied by the auxiliary pump.

We need to know how long it will take the auxiliary pump to empty the remaining 1 4 tank which the main pump cannot empty in the 3 hours. The auxiliary pump’s rate is 1 9 tanker per hour. Let X be the number of hours it takes the auxiliary pump to empty the 1 4 tank which the main pump will not be able to empty in the 3 hours allotted.

(rate in tankers per hour)(time required) = 1 4 tank

( 1 9 )x= 1 4

Therefore 4x=9 .

x= 9 4

x=2 1 4

x= 2 hours 15 minutes.

So the auxiliary tank must be started 2 hours 15 minutes before 12 noon, so it must started at 9:45 AM.

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