Two water taps together can fill a tank in 178 hours. The tap with longer diameter takes 2 hours less than the tap with smaller one to fill the tank separately. Find the time in which each tap can fill the tank separately.
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Solution
Given two taps can fill a tank in 178=158 hours
Amount of water filled by two taps in 1 hour is 1158=815
Let the time taken by longer diameter tap to fill the tank be x hrs
the time taken by other tap to fill the tank be y hrs
from the given condition
x=y−2
Amount of water filled by longer diameter tap in 1 hour is 1x=1y−2
Amount of water filled by longer diameter tap in 1 hour is 1y
⟹1y−2+1y=815⟹4y2−23y+15=0⟹y=34,5
⟹x=−54,3 but x=−54 is not possible
So x=3,y=5
the time taken by longer diameter tap to fill the tank be 3 hrs
the time taken by other tap to fill the tank be 5 hrs