A can lay a railway track in 16 days and B in 12 days. With help of C they finish the job in 4 days. In how many days can C alone do the job?

Problem restatementCompute C’s rate from the combined rate and A, B rates; then invert to get C’s solo time.

Given data

• A: 16 days ⇒ 1÷16 per day
• B: 12 days ⇒ 1÷12 per day
• A + B + C: 4 days ⇒ 1÷4 per day

Concept/ApproachUse linearity of rates: r_C = r_ABC − r_A − r_B.

Step-by-step calculationr_C = 1÷4 − 1÷16 − 1÷12= 12÷48 − 3÷48 − 4÷48 = 5÷48 per dayTime for C alone = 48÷5 = 9⅕ days (9.6 days)

Verification/AlternativeSum rates: 1÷16 + 1÷12 + 5÷48 = 3÷48 + 4÷48 + 5÷48 = 12÷48 = 1÷4.

Common pitfallsDo not average days; always add rates.

Final Answer9⅕ days