Question

a tank can be filed by big pump in 20 hours and by small pump in 80 hours how long will it take to fill the tank by both pumps together

Answer 1

rate * time = quantity or work produced. 

rate is in fraction of the pope filled in one hour.
time is in hours.
quantity is one full pipe. 

for big pump, this formula becomes rate * 80 = 1
solve for rate to get rate of big pipe = ability to fill 1/80 of the pipe per hour. 

for little pump, this fornmla becomes rate * 40 = 1
solve for rate to get rate of little pipe = ability to fill 1/40 of the pipe per hour. 

when they work together, their rates are additive. 

you get (1/40 + 1/80) * time = 1 

1/40 * 2/2 = 2/80. 

(2/80 + 1/80) * time = 1 becomes 3/80 * time = 1 

solve for time to get time = 1/(3/80) = 1 * 80/3 = 26 and 2/3 hours. 

when they work together they can fill the pipe in 26 and 2/3 hours. 

to confirm: 

rate of 3/80 of the pipe per hour times 80/3 hours = 1 full pipe. 

Answer 2

the time will be
=80/20
=4hours
the time is 4 hours
see if the big need 20 h
and both take time of 4 h so for small one
we will do 4×20=80
this proves that answer is right