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)?

machines A, B and C complete job in 44 hours

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

and

8b + 15c =        ....................2

now add both these equation 1 and 2

15a + 7b + 8b + 15c =     +  

15a + 15 b + 15c =  

solve we get

a + b + c =

here combine work in    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