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Three printing presses, R, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take R, working alone at its constant rate, to do the same job?

A. 8
B. 10
C. 12
D. 15
E. 20

Respuesta :

Answer:

20(E)

Step-by-step explanation:

Printing press R, S and T are working together at their respective constant rate.

They can do a job for 4 hours.

Let r, s and t be the time for printing press R, S and T to complete the job alone at their respective constant rate.

Rate of printing press R = 1/r

Rate of printing press S = 1/s

Rate of printing press T = 1/t

Rate = job / time

R + S + T = 4

1/r + 1/s + 1/t = 1/4

S + T = 5

1/s + 1/t = 1/5

Substitute 1/s + 1/t = 1/5 in the equation 1/r + 1/s + 1/t = 1/4

1/r + 1/5 = 1/4

1/r = 1/4 - 1/5

1/r = (5 - 4)/ 20

1/r = 1/20

r = 20 hours

It takes the printing press R 20 hours to complete the job alone

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