Two water taps together can fill a tank in
[tex]1 \frac{7}{8} \: hours[/tex]
The tap with larger diameter takes 2 h less than the tap with smaller one to fill the tanks separately. Find the time in which both the taps can fill the tank separately.
AND
A motorboat covers a distance of 16 km upstream and 24 km downstream in 6 hours. If the same time it covers a distance of 12 km upstream and 36km downstream. Find the speed of boat lin still water and that of the stream.
[tex]1 \frac{7}{8} \: hours[/tex]
The tap with larger diameter takes 2 h less than the tap with smaller one to fill the tanks separately. Find the time in which both the taps can fill the tank separately.
AND
A motorboat covers a distance of 16 km upstream and 24 km downstream in 6 hours. If the same time it covers a distance of 12 km upstream and 36km downstream. Find the speed of boat lin still water and that of the stream.
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Answer:
Given two taps can fill a tank in 1
8
7
=
8
15
hours
Amount of water filled by two taps in 1 hour is
8
15
1
=
15
8
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
x
1
=
y−2
1
Amount of water filled by longer diameter tap in 1 hour is
y
1
⟹
y−2
1
+
y
1
=
15
8
⟹4y
2
−23y+15=0⟹y=
4
3
,5
⟹x=−
4
5
,3 but x=−
4
5
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
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