Two Water Taps Together Can Fill a Tank in 1 7 8 Hours. the Tap with Longer Diameter Takes 2 Hours Less than the Tap with a Smaller One to Fill the Tank Separately.
Answers
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 and hrs
from the given condition
x=and−2
Amount of water filled by longer diameter tap in 1 hour is
x
1
=
and−2
1
Amount of water filled by longer diameter tap in 1 hour is
and
1
⟹
and−2
1
+
and
1
=
15
8
⟹4 y
2
−2 3 y+15=0⟹and=
4
3
,5
⟹x=−
4
5
,3 but x=−
4
5
is not possible
So x=3,and=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
Answer:
Step-by-step explanation:
The two taps can together fill the tank in = 1
So, in 1 hr, the two taps together will fill = of the tank
Let the tap with smaller diameter alone fill the tank in "x" hrs, then the tap with longer diameter will fill the tank in "(x - 2)" hrs.
So, the part of the tank filled by each of the taps separate in 1 hr will be,
Smaller tap:
Longer tap:
Therefore, we have the final eq. as,
⇒
⇒
⇒
⇒ 15x - 15 = 4x² - 8x
⇒ 4x² - 23x + 15 = 0
⇒ 4x² - 20x - 3x + 15 = 0
⇒ 4x(x - 5) - 3(x-5) = 0
⇒ (x - 5)(4x -3) = 0
⇒ x = 5 or
neglecting the x = because the the time taken by longer tap will be negative
⇒ x = 5 hrs ← time taken by the tap with smaller diameter to fill the tank separately
∴ x - 2 = 5 - 2 = 3 hrs ← time taken by the tap with longer diameter to fill the tank separately