How long would it take them to work together?

Question

A grocery needs to prepare a large order of deli trays for a big football weekend. It would take Henry 10.1 hours to prepare the trays. Felipe can complete the job in 12.1 hours. How long would it take? them, working? together, to prepare the? trays?

Answer 1

Let x = the time taken for both Henry and Felipe to prepare the trays.

 

Therefore, amount of work (unit rate) done per hour = 1/x

 

Assuming they work at a constant rate, then,

 

Work done by Henry in 1 hour + Work done by Felipe in 1 hour = Work done by both men in 1 hour

 

(1/10.1) + (1/12.1) = 1/x

 

LCD of all denominators = (10.1)(12.1)x = 122.21x

 

Multiply each side by 122.21x:

 

122.21x[(1/10.1) + (1/12.1)] = 122.21x(1/x)

 

                     12.1x + 10.1x = 122.21

 

                                  22.2x = 122.21

 

                                        x = 122.21/22.2

                 

                                        x = 5.5

 

Therefore, it will take them 5.5 hours to prepare the trays if they work together.