Question

A large inlet pipe can fill a tank 16 minutes faster than a smaller pipe. When both inlets are used, the tank fills in 6 minutes. How long does it take the smaller inlet pipe working alone to fill the tank?

Answer 1

let x be the time it takes for the smaller pipe to fill the tank (alone)
therefore it takes x+ 16 for the bigger pipe

now we use the formula \[\frac{t}{a} +\frac{t}{b} = 1\]
where a and b are the individual time and t is the total time

it says the total time here is 6 minutes so
\[\frac{6}{x} + \frac{6}{x+ 16} = 1\]
now solve for x

Answer 2

let rate of work for small pipe be 1/p
then rate of work for big pipe is 1/(p+16)
then if they work for 6 min the work is done
that is ,
p cannot be negative so
p = 8 min