Question

Working together, Kendra, Latasha, and Melanie can complete a certain task in 4 hours. If
Kendra alone could complete the task in 8 hours and Latasha could complete the task in half
the time it would take Melanie, how long would it take Latasha to complete the task by herself?​

Answer 1

Solution :

Kendra alone can complete the task in 8 hours .

So , the part of the task that's she can complete in 1 hr

=> ⅛ th .

Let us assume that it takes Melanie x hours to complete the task ( alone )

So , she can complete 1/x th of it in 1 hr.

Latasha can complete it in half the time taken by Melanie .

So , amount of work done by her in 1 hr

=> 2/x .

Now ;

⅛ + 1/x + 2/x = ¼

=> 1/x + 2/x = 1/4 - 1/8

=> 1/x + 2/ x = 2/8 - 1/8

=> 1/x + 2/x = ⅛

=> 1/x [ 1 + 2 ] = ⅛

=> 3/x = ⅛

=> x = 24 hours .

So , Melanie takes 24 hours to complete the task .

It will take Latasha , half the time i.e 12 hours to do it .

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