Respuesta :
Answer:
20 hours
Step-by-step explanation:
We can work easier if we think in terms of an hour
the first equation that we can write is
A + B = 1/4 (its meaning is that in an hour A and B fill 1/4 of the cistern)
the second equation we can write is
A + C = 1/5 (its meaning is that in an hour A and C fill 1/5 of the cistern)
the third equation that we can write is
B = 2C (its meaning is that in an hour B fill 2 times C the cistern)
now we can substitute the value of B in the first two equations
A + 2C = 1/4
A + C = 1/5
A = 1/5 - C
1/5 - C + 2C = 1/4
C = 1/4 -1/5
C = (5-4)/20
C = 1/20 (this means that in an hour C will fill 1/20 of the cistern, so it takes 20 hours to fill the entire cistern)
A = 1/5 - 1/20
A = (4-1)/20 = 3/20
B = 1/20 *2 = 1/10
A and B can fill a cistern in 4 hours. A and C can fill the same cistern in 5 hours and C would take to fill the cistern 20 hours
We can work easier if we think in terms of an hour
The first equation that we can write is
What is the first equation?
A + B = 1/4 (its meaning is that in an hour A and B fill 1/4 of the cistern)
The second equation we can write is
A + C = 1/5 (its meaning is that in an hour A and C fill 1/5 of the cistern)
The third equation that we can write is
B = 2C (its meaning is that in an hour B fill 2 times C the cistern)
now we can substitute the value of B in the first two equations
A + 2C = 1/4
A + C = 1/5
A = 1/5 - C
1/5 - C + 2C = 1/4
C = 1/4 -1/5
C = (5-4)/20
C = 1/20 (this means that in an hour C will fill 1/20 of the cistern, so it takes 20 hours to fill the entire cistern)
A = 1/5 - 1/20
A = (4-1)/20 = 3/20
B = 1/20 *2 = 1/10
A and B can fill a cistern in 4 hours. A and C can fill the same cistern in 5 hours and C would take to fill the cistern 20 hours.
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