Question

Two water taps together can fill a tank in 11 1/9 hours. The tap of larger diameter takes 5 hours less thsn the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank. ​

Answer 1

ANSWER

let the smaller diameter tap alone fill the tank in x hours...

and larger diameter tap fill it in x−8 hours

so

when they work toghether

smaller tap fills 1/x in one hour

larger tap fills 1/x−8 in one hour

toghether they fill in

1/x+1/(x−8) in one hour..

time taken by both =9 hours 36min

=9+36/60 hours ( and by cancelling )

=9+3/5

both toghether fills it in

9/5 hours ( change into mixed fraction)

=48/5 hours

there from data given

1/x+1/x−8=5/48

1/x+1/x−8=5/48

by calculating

5x

2

−136x+384=0

x=(136+ or −104)/10

=x=24 or x=16/5

toghether.

x=24 hours (smaller tap)

bigger tap =x−8=16 hours

24 hours whereas bigger tap takes 16hours.