SOLUTION: please help 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 9am , when should the auxil

Question 264824: please help
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 9am , when should the auxiliary pump be started so that the tanker is emptied by noon?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
main pump equals 4 hours.
aux pump equals 9 hours.
start at 9:00 am and want to end at 12:00 pm.
total of 3 hours.

rate * time = units

the units are 1 tank.

main pump can empty the tank in 4 hours so x*4 = 1 which means that the main pump can empty 1/4 of the tank in 1 hour.
the aux pump can empty the tank in 9 hours so x*9 = 1 which means that the aux pump can empty 1/9 of the tank in 1 hour.

the main pump starts at 900 am.

the total time allowed is 3 hours.

the main pump alone would therefore empty 3 * 1/4 = 3/4 of the tank in 3 hours.

that means that 1/4 of the tank still needs to be emptied.

the aux pump can empty 1/4 of the tank in how many hours?

the formula is rate * time = units of work.

we get 1/9 * x = 1/4 where x is the amount of time it will take the aux tank to empty 1/4 of the tank.

formula is:

1/9 * x = 1/4

multiply both sides of this equation by 9 to get:

x = 9/4 hours.

9/4 hours is the same as 2 + 1/4 hours.

subtract that from 12 pm and you get 9 + 3/4 hours is when the aux pump should be started.

90 + 3/4 hours is the same as 9:45 am.

here's what happens.

at 9:00 am the main pump starts pumping.

at 9:45 am the aux pump starts pumping.

by 12:00 pm the main pump has pumped 1/4 * 3 = 3/4 of the tank.
by 12:00 pm the aux pump has pumped 1/9 * 9/4 = 1/4 of the tank.

3/4 + 1/4 = 1 which means the tank is empty at 12:00 pm.

RELATED QUESTIONS
An oil tanker can be emptied by the main pump in 4 hours.An auxiliary pump can empty the... (answered by josgarithmetic,ikleyn)

An oil tanker can be emptied by the main pump in 4 hours. An auxiliary pump can empty the (answered by ankor@dixie-net.com)

An oil tanker can be emptied by the main pump in 4 hours. An auxiliary pump can empty the (answered by lwsshak3)

An oil tanker can be emptied by the main pump in 4 hours.An auxiliary pump can empty the... (answered by ikleyn)

an oil tanker can be emptied by the main pump in 4 hours. an auxiliary pump can empty the (answered by stanbon)

An oil tanker can be emptied by the main pump in 4 hours. An auxiliary pump can empty the (answered by josmiceli)

an oil tanker can be emptied by the main pump in four hours. an auxilary pump can empty... (answered by scott8148,Edwin McCravy)

An oil tanker can be emptied by the main pump in 4 hours and by an auxiliary pump in 9... (answered by ptaylor)