Algebra 2 question?

Question

Jena and Cara, working together, can rake the yard in 5 hours. Working alone, Cara takes five times as long as Jena. How long does it take Jena to rake the yard alone?

Answer 1

Let J & C be the  time taken for John & Cara to rake the lawn.

 

C = 5J 

 

J + C = 5 hours

 

Now substitute for C into the equation that we have above ^^

 

J + 5J = 5

 

6J =  5

 

J = 5/6

 

5 hours is 300 minutes so 5/6 would be 300/6 which is 50 minutes

 

Jenna takes 50 minutes to rake the lawn.

Answer 2

The key to this class of problems is that rates add.   

 

If  C is Cara's rate of yard work (number of yards done per hour)  and Jena's rate is J,

 

the problem statements can be translated as

 

   C + J = 1/5    and

   C  =  J/5

 

Solving these together yields    C = 1/30  and J =  1/6

 

Since Jena's rate is 1/6 of a yard done per hour,  it will take her 6 hours to do the whole yard.