SOLUTION: A tank can be filled by two pipes separately in 10 and 15 minutes respectively. When a third pipe is used simultaneously with the first two pipes, the tank can ve filled in 4 minut

Question 551382: A tank can be filled by two pipes separately in 10 and 15 minutes respectively. When a third pipe is used simultaneously with the first two pipes, the tank can ve filled in 4 minutes. How long it take the third pipe alone to fill the tank? Please, thank you~ :) Happy new year, to all Tutors and Students! <3
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
pipe 1 can fill the tank in 10 minutes.
pipe 2 can fill the tank in 12 minutes.
pipe 3 can fill the tank in x minutes.
when they all work together, they can fill the tank in 4 minutes.
the basic formula is:
rate * time = units.
the number of units is equal to 1 (the tank).
the rate for pipe 1 = 1/10 of the tank in 1 minute.
the rate for pipe 2 = 1/12 of the tank in 1 minute.
the rate for pipe 3 = 1/x of the tank in 1 minute.
when they work together, their rates are additive, so you get:
(1/10 + 1/12 + 1/x) * 4 = 1
simplify this to get:
4/10 + 4/12 + 4/x = 1
multiply both sides of this equation by an LCM of 60*x to get:
4*60*x/10 + 4*60*x/12 + 4*60*x/x = 1*60*x
simplify this to get:
24*x + 20*x + 240 = 60*x
combine like terms to get:
44*x + 240 = 60*x
subtract 44*x from both sides of this equation to get:
240 = 16*x
divide both sides of this equation by 16 to get:
x = 15.
the third pipe can fill the tank in 15 minutes.
to confirm, we go back to the original equation that states that all 3 pipes working together can fill the tank in 4 minutes.
the rates of the pipes are:
pipe 1 = 1/10
pipe 2 = 1/12
pipe 3 = 1/15
the formula of rate * time = units becomes:
(1/10 + 1/12 + 1/15)*4 = 1
simplify to get:
4/10 + 4/12 + 4/15 = 1
multiply both sides of this equation by 60 to get:
24 + 20 + 16 = 60
simplify to get:
60 = 60
this confirms that the value of x is good and that the third pipe can fill the tank in 15 minutes working alone.

RELATED QUESTIONS
A tank can be filled by two pipes separately in 10 and 15 minutes respectively. When a... (answered by mangopeeler07,ankor@dixie-net.com)

A tank can be filled by two pipes separately in 10 and 15 minutes respectively. When a... (answered by lwsshak3)

A tank can be filled by two pipes separately in 10 and 15 minutes respectively. When a... (answered by stanbon)

Hello Masters in math, can you help me to solve my assignments in algebra Regards,... (answered by mananth)

A tank can be filled in 12 minutes by two pipes running simultaneously. By the larger... (answered by josmiceli)

a tank can be filled by one pipe in 20 minutes and it can be filled by a second pipe in... (answered by psbhowmick)

A tank may be filled using pipe A and B with times of 12 and 20 minutes respectively. It... (answered by stanbon)

Two pipes can be used to fill a water tank. If used alone the first pipe could fill the... (answered by partha_ban)

A tank can be filled by one pipe in four hours and by a second pipe in six hours;and when (answered by ankor@dixie-net.com)