Pertanyaan

If A, B, and C working together can do a certain task in 6 hours. A and B can do the task in 9 hours, and B and C can do the task in 12 hours. How long would it take if each of them working alone to do the task?

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M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Pembahasan

Let x is amount of time needed for A do do the task working alone. Then A works at the rate of of the task per hour. Let y is amount of time needed for B to do the task working alone. Then B works at the rate of of the task per hour Let z is amount of time needed for C to do the task working alone. Then C works at the rate of of the task per hour. If A, B, and C working together can do a certain task in 6 hours A and B can do the task in 9 hours: B and C can do the task in 12 hours Substitute (1) to (2) Time needed for C working alone is 18 hours Substitute value of z to (3) Time needed for B working alone is 36 hours Substitute value of z to (2) Time needed for A working alone is 12 hours

Let x is amount of time needed for A do do the task working alone. Then A works at the rate of 1 over x of the task per hour.
Let y is amount of time needed for B to do the task working alone. Then B works at the rate of 1 over y of the task per hour
Let z is amount of time needed for C to do the task working alone. Then C works at the rate of 1 over z of the task per hour.

If A, B, and C working together can do a certain task in 6 hours

1 over x plus 1 over y plus 1 over z equals 1 over 6... open parentheses 1 close parentheses

A and B can do the task in 9 hours:

1 over x plus 1 over y equals 1 over 9... open parentheses 2 close parentheses

B and C can do the task in 12 hours

1 over y plus 1 over z equals 1 over 12... open parentheses 3 close parentheses

Substitute (1) to (2)

Time needed for C working alone is 18 hours

Substitute value of z to (3)

1 over y plus 1 over z equals 1 over 12 1 over y plus open parentheses 1 over 18 close parentheses equals 1 over 12 1 over y equals 1 over 36 y equals 36

Time needed for B working alone is 36 hours

Substitute value of z to (2)

1 over x plus 1 over y equals 1 over 9 1 over x plus open parentheses 1 over 36 close parentheses equals 1 over 9 1 over x equals 1 over 12 x equals 12

Time needed for A working alone is 12 hours

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