Question

P is 4 times faster than Q in doing a job. Q takes 27 more days than P to finish the job. If they work together, in how many days will the work be finished

Answer 1

Answer:

36/5 days or 7 \times \frac{1}{5} days

Step-by-step explanation:

Rate(P) = 4 × Rate(Q)

let the total work be = 1 unit

Using, Rate × Time = Work

Time taken by P = 1/Rate(P) = Time(P)

Time taken by Q = 1/Rate(Q) = Time(Q)

Time(Q) - Time(P) = 27

[1/Rate(Q)] - [1/Rate(P)] = 27

[Rate(P) - Rate(Q)]/[Rate(P) × Rate(Q)] = 27

[(4 × Rate(Q)) - Rate(Q)]/[(4 × Rate(Q)) × Rate(Q)] = 27

[3 × Rate(Q)]/[(4 × Rate(Q)) × Rate(Q)] = 27

Rate(Q)/[(4 × Rate(Q)) × Rate(Q)] = 9

1/[4 × Rate(Q)] = 9

1 = 36 × Rate(Q)

Rate(Q) = 1/36

Therefore, Rate(P) = 4 × 1/36 = 1/9

Rate(P) + Rate(Q) = (1/36) + (1/9)

= 5/36 = Rate(P + Q)

Using, Rate × Time = Work

Rate(P + Q) Time(P + Q) = Total Work

(5/36) × Time(P + Q) = 1

Time(P + Q) = 36/5 =

Therefore, if P and Q work together, they will finish work in 36/5 days or days

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