Asked by AlfredMaths 💯

Tom and Ben working together can finish a piece of work in 3 days. Tom can finish it alone in 4 days. Find the time Ben required to finish the work by himself?

Mary Rodriguez

Passionate about Business, Economics and Careers Guidance

This scenario can be written as a simultaneous equation. If we write Tom's output per day as T and Ben's output per day as B. If we know Tom does his job alone in 4 days, his output per day is 1 job divided by 4 days = 0.25 jobs per day. So let's say T = 0.25. Based on that we can say: 4T = 1. So T = 1/4. When they both work together we can write this as: 3B + 3T = 1. This is because Ben gives 3 days of output, so 3B, and Tom also gives 3 days of output, so 3T. And together, that equals 1 complete job. Since we know T = 1/4, let's substitute that into the second equation. 3B + 3*(1/4) = 1 3B + 3/4 = 1 3B = 1 - 3/4 3B = 1/4 B = 1/(4*3) B = 1/12 So if Ben's output is 1/12 per day, it would take him 12 days to reach 1. So, the answer is 12 days.

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