A hard question on work problems for P5, with a step-by-step solution, diagrams and the answer. Common in the Hua Xia Cup's P3 to P6 papers; harder ones have someone leaving partway, people taking turns, or cows grazing a field that keeps growing.
The question
An estate is laying a new cycle track, with teams A and B on the job.
What team A does in 1 day takes team B 2 days.
Working together the two teams would finish in 28 days.
In fact team A works alone for the first 3 days, then team B joins and they finish it together.
Each team works at a steady pace.
How many days does the job take from start to finish?
Show the hints (3)
💡Hint 1: How do the two teams' daily amounts compare? Which is faster?
💡Hint 2: Say team A does 2 parts a day and team B 1. How many parts is the whole job?
💡Hint 3: The job is 84 parts. How many are left after team A's 3 days alone?
Worked solution
Have a go first, then read the solution step by step.
1.1 day of A = 2 days of B, so their daily amounts are A : B = 2 : 1. Say A does 2 parts a day and B 1.
2.Together they do 2 + 1 = 3 parts a day and take 28 days: the job = 3 × 28 = 84 parts.
Play more like this in Numsprite (unlimited questions, instant marking) →A free maths game: every level free from Easy to Expert (★ to ★★★★), unlimited questions, no download