working alone,it takes mofor nine hours to tar a roof.emily can tar the same roof in 8 hours.how long would it take them if they worked together?

Question

 help please

 

Answer 1

The exercise here is understanding fractions and keeping track of units. In this question, what units are you looking for? You're looking for the length of time. You just have to set it up.

 

It takes Mofor 9 [hours / roof] (read as 9 hours per roof).

It takes Emily 8 [hours / roof].

 

If you flip the expressions:

 

Mofor finishes 1/9 [roof / hour] (read as 1/9 of a roof per hour).

Emily finishes 1/8 [roof / hour].

 

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Sidenote: these are called rates. If you see the word "per", it's a rate, and you should see a division line.

Example: Miles per hour = [mi / hr]

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You already know that it takes Mofor 9 hours to do a roof.

1/9 [roof / hour] * 9 [hours] = 1 roof

 

Likewise, Emily finishes a roof in 8 hours.

1/8 [roof / hour] * 8 [hours] = 1 roof

 

If they both worked together, they each contribute part of their work to complete 1 roof.

(1/9 + 1/8) [roof / hour] * h [hours] = 1 roof

 

Solve for h.