SOLUTION: 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 s

Question 1207783: 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?

My equation:
(x/4) + (x/9) = 1

Yes?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39613)   (Show Source): You can put this solution on YOUR website!
The pumping rates:
Main, units of Tanks per Hour
Auxiliary, Tanks per hour

(?)

t amount of time with only main pump
v amount of time both pumps together

The whole amount of time for emptying the tank from 9am to noon is 3 hours.

This would seem to give a system of equations
.

Simplify the first equation, take second equation and substitute for v, into the first (now simplified) equation.

Thinking again what I said, maybe easier to use elimination method, unless I already made a mistake somewhere...

and question asks essentially for t.

-------------------9:45 AM
Answer by ikleyn(52752)   (Show Source): You can put this solution on YOUR website!
.
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?

My equation:
(x/4) + (x/9) = 1

Yes?
~~~~~~~~~~~~~~~~~~~~~~~

        Your equation is incorrect.

        It is inapplicable to this problem.

        This problem can be solved mentally, without using any equations.

According to the schedule, the main pump drains the oil during 3 hours (from 9 am to the noon). During this time, it makes of the job. Hence, of the job should be performed by the auxiliary pump. The auxiliary pump has the rate of work of the job per hour. To make of the job, this auxiliary pump needs = hours = 2 hours. It means that the auxiliary pump should start working 2 hours before the noon. ANSWER. The auxiliary pump should start working at 9:45 am.

Solved (mentally).

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