SOLUTION: Hello Tutors, I am having trouble answering two questions: 1. An oil tanker can be emptied by the main pump in 5 hours. An auxiliary pump can empty the tanker in 14 hours. I

Question 1095618: Hello Tutors,
I am having trouble answering two questions:

1. An oil tanker can be emptied by the main pump in 5 hours. An auxiliary pump can empty the tanker in 14 hours. If the main pump is started at 5pm, When should the auxiliary pump be started so that the tanker is emptied by 9pm?
2. A gardener has 97 feet of fencing to be used to enclose a rectangular garden that has a border 2 feet wide surrounding it. if the length and width of the garden are to be the same, what would be the dimension of the garden?(length and width)
Thank you in advance for your help.

Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
If the main pump is started at 5 and it runs until 9, then the problem is telling us the main pump will run 4 hours, so we just need to find out how long the auxiliary pump has to run, I'll call this x:
Main pump can empty tank in 5 hours but will run 4 and 4 out of 5 = 4/5
Add the time the auxiliary pump will run, it will run x hours and could empty the tank by itself in 14: x/14 Add the two together:
4/5 + (x/14) = 1
x(1/14) = 1 - 4/5
x(1/14) = 1/5
x = 1/5(14)
x = 2.8 hours = 2(.8*60) = 2hours 48 minutes. This is how long the auxiliary pump has to run in order for the two pumps to empty the tanker by 9. Subtract 2h 48min from 9 to get your answer.

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