Ratios and relationships

Question

If 6 people take 3 days to dig 8 ditches, then how long would it take 4 people to dig 10 ditches? Assume that all the ditches are the same size and take equally long to dig, and that all people work at the same steady rate. Explain how to reason about multiplication and division with quantities to solve this problem.

Answer 1

6 take 3 to dig 8

1 takes times as long as 6 people = 6x3 = 18 days to dig 8 ditches

1 takes 8/18 = 4/9 days to dig 1 ditch

4 take (4/9)/4 = 1/9 day to dig 1 ditch

4 take 10(1/9) = 10/9 days to dig 10 ditches or 10 days and 24/9 = 8/3 = 2 hours and 40 minutes

4 people take 10 days, 2 hours and 40 minutes to dig 10 ditches