Ken can write all the boring word problems for this book in l0 hours.After he has worked 2 hours, Steve comes to help him and together they finish the problems in 3 more hours. How many hours...

Ken can write all the boring word problems for this book in l0 hours.
After he has worked 2 hours, Steve comes to help him and together they finish the problems in 3 more hours. How many hours would it have taken steve
working aloneP

Asked on by ltop

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tiburtius's profile pic

tiburtius | High School Teacher | (Level 2) Educator

Posted on

Ken needs 10 hours to finish the job so in one hour he can do `1/10` of the job. After he's been working for 2 hours there are still `8/10` of the job unfinished which he and Steve finish in 3 hours.

`8/10=3cdot1/10+3cdot s`  

`s` is the amount of work done by Steve in one hour.

`3s=8/10-3/10`

`3s=1/2`

`s=1/6`  

So in one hour Steve can do `1/6` of the job hence he would finish the job in 6 hours if he worked alone. 

tonys538's profile pic

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

Ken can write all the boring word problems for a book in 10 hours. The rate at which he can complete the work is W/10.

In two hours the work, completed by him is (W/10)*2 = W/5.

He is helped by Steve with whom he finishes the work in 3 hours. Let the rate at which Steve works be W/x.

Now (W - W/5)/(W/10 + W/x) = 3

(1 - 1/5)/(1/10 + 1/x) = 3

4/5 = 3*(1/10 + 1/x)

3/x = 4/5 - 3/10

3/x = 5/10

x = 6

On his own Steve would have required 6 hours to complete the work.

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