College Algebra

Question

An oil tanker can be emptied by the main pump in 4 hours. An auxiliary pump can empty the tanker in 6 hours. If the main pump is started at 8 PM, when should the auxiliary pump be started so that the tankers empty by 11 PM?

Answer 1

start the Auxilary at 9:30 pm to completely empty the tanker by 11pm

M empties in 4 hours A empties in 6 hours alone

Main emptier will empty 1/4 per hour. in 3 hours from 8 to 11, it will empty (11-8)(1/4) = 3/4

leaving 1/4 to be emptied by A

calculate how many hours A needs to complete 1/4 of the tanker

it does 1/6 per hour

h/6 = 1/4

h/3 = 1/2

h= 3/2 =1.5 hours

11pm - 1.5 = 9:30 pm

in 3 hours Main empties 3/4, 8 to 11

in 1.5 hours Auxiliary empties (3/2)(1/6 = 1/4 9:30 to 11

3/4 + 1/4 = 1, completely emptying the tanker