Question

Together, 15 Type A machines and 7 Type B machines can complete a certain job in 4 hours. Together, 8 Type B machines and 15 Type C machines can complete the same job in 11 hours. How many hours would it take one Type A machine, one Type B machine, and one Type C machine working together to complete the job (assuming constant rates for each machine)?

Answer 1

machines A, B and C complete job in 44 hours

Step-by-step explanation:

given data

15 A machines and 7 B machines = 4 hours

8 B machines and 15 C machines = 11 hours

to find out

How many hours take one A machine, one B machine and one C machine working together to complete the job

solution

we consider here rates of machines A, B and C are a, b, and c respectively

so equation will be when work together

15a + 7b =
`(1)/(4)` ...................1

and

8b + 15c =
`(1)/(11)` ....................2

now add both these equation 1 and 2

15a + 7b + 8b + 15c =
`(1)/(4)` +
`(1)/(11)`

15a + 15 b + 15c =
`(15)/(44)`

solve we get

a + b + c =
`(1)/(44)`

here combine work in
`(1)/(44)` jobs per hours

so here we know time is reciprocal of the rate

so that machines A, B and C complete job in 44 hours