Question

Mai, Clare, and Noah are making signs to advertise the school dance. It takes Mai 6 minutes to complete a sign, it takes Clare 8 minutes to complete a sign, and it takes Noah 5 minutes to complete a sign. They keep working at the same rate for a half hour.

Will Mai and Clare complete a sign at the same time? Explain your reasoning.
Will Mai and Noah complete a sign at the same time? Explain your reasoning.
Will Clare and Noah complete a sign at the same time? Explain your reasoning
Will all three students complete a sign at the same time? Explain your reasoning

Answer 1

Mai and Clare will complete the fourth and third signs respectively at 24 minutes after beginning the task

Mai and Noah won´t finish signs at the same time

Clare and Noah won´t finish signs at the same time

Explanation:

A) During half an hour of work

Mai will finish signs at:

6 12 18 24 32 ( out of the range of 1/2 hour)

for Clare finishing time are:

8 16 24 32 out

And Noah

5 10 15 20 25 30 no more

Mai and Clare will complete the fourth and third signs respectively at 24 minutes after beginning the task

Mai and Noah won´t finish signs at the same time

Clare and Noah won´t finish signs at the same time

We can give answers to that type of question, just by examining the products of time making the sign * each different sign, as we did.

In fact, 24 is the minimum common multiple of 6 and 8

6 * 4 = 24

8 * 3 = 24

And that is the required condition to get finished signs at the same time.