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

Answer:

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

Step-by-step 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.