let A = flow rate for tap A in units per hour
(2 hrs)(A + 2A + 3A) + (2.75 hrs)(A + 3A) = 1 tub filled
23A = 1
A = (1 tub filled)/(23 hrs)
using all 3 ...
(A + 2A + 3A)t = 1 tub filled
solve for t
Could anyone help me with this problem please?
Archimedes has a bath which is filled using three taps labelled A, B and C.
The rates of flow of B is twice that of A, the rates of flow of C is three times that of A.
Yesterday, Archimedes filled his bath as follows:
Firstly he used all three taps for 2 hours. Then he turned off B and finished filling the bath in an additional 2 hours and 45 mins using taps A and C only (it's a very big bath).
Today Archimedes is going to fill his bath (currently empty) using all three taps.
How long will this take him?
Hello, Natasha1!
Archimedes has a bath which is filled using three taps labelled A, B and C.
The rate of flow of B is twice that of A; the rate of flow of C is three times that of A.
Yesterday, Archimedes filled his bath as follows:
First, he used all three taps for 2 hours. Then he turned off B and finished filling the bath
in an additional 2 hours and 45 mins using taps A and C only.
Today Archimedes is going to fill his bath (currently empty) using all three taps.
How long will this take him?
Let = number of hours for A to fill the bath alone.
In one hour, A can fill of the bath.
Then B can fill the bath alone in hours.
In one hour, B can fill of the bath.
And C can fill the bath alone in hours.
In one hour, C can fill of the bath.
In hours, the three taps can fill: of the bath.
In hours, A and C can fill: of the bath.
These two quantities can fill the entire bath: .
. . Hence: .
A takes hours to fill the bath.
. . In one hour, A fills of the bath.
. . In hours, A fills of the bath.
B takes hours to fill the bath.
. . In one hour, B fills of the bath.
. . In hours, B fills of the bath.
C takes hours to fill the bath.
. . In one hour, C fills of the bath.
. . In hours, C fills of the bath.
In hours, the three taps will fill the entire bath.
. .
. .
Therefore, the three taps will take hours.