Two water taps together can fill a tank in 9 hours 36 minutes. The tap of larger diameter takes 8 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
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Answer:
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Step-by-step explanation:
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.
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