SOLUTION: . Peter and Steven take 5 1/3 hours to do a job. Steven alone takes 16 hours to do the same job. How long would it take Peter to do the same job alone?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: . Peter and Steven take 5 1/3 hours to do a job. Steven alone takes 16 hours to do the same job. How long would it take Peter to do the same job alone?      Log On


   

Question 1179401: . Peter and Steven take 5 1/3 hours to do a job. Steven alone takes 16 hours to
do the same job. How long would it take Peter to do the same job alone?
Found 4 solutions by josgarithmetic, ikleyn, mananth, greenestamps:
Answer by josgarithmetic(39618) About Me  (Show Source):
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
Peter and Steven take 5 1/3 hours to do a job. Steven alone takes 16 hours to
do the same job. How long would it take Peter to do the same job alone?
~~~~~~~~~~~~~ 

Notice that  5 1/3 hours is  16%2F3  hours.


So, their combined rate of work is  1%2F%28%2816%2F3%29%29  = 3%2F16  of the job per hour.


Steven's rate of work is  1%2F16  of the job per hour.


Hence, Peter's rate of work is the difference  3%2F16 - 1%2F16 = 2%2F16 = 1%2F8  of the job per hour.


It implies that Peter will complete the job in 8 hours, working alone.    ANSWER

Solved.

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It is a standard and typical joint work problem.

There is a wide variety of similar solved joint-work problems with detailed explanations in this site.  See the lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive


Read them and get be trained in solving joint-work problems.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic
"Rate of work and joint work problems"  of the section  "Word problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.


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Notice that  @Mananth calculated incorrectly in his post,

THEREFORE,  his  (or her)  solution and the answer  BOTH  are  WRONG.


Simply ignore it,  for your safety . . .



Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Peter and Steven take 5 1/3 hours to do a job.===> 16/3 hours
In 1 hour they do 3/15 of the job
Steven does the same job alone in16 hours
So he does 1/16 of job in 1 hour
Let peter take x hours to do the job alone
he does 1/x of the job in 1 hour
1/x + 1/16 = 3/15
1/x = 3/15 -1/16
1/x = 16*3- 15/15*16
1/x =33/15*16
x 15*16/33
=7.23 hours
peter take 7.23 hours to do the job alone

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The formal algebraic solutions shown by the other tutors, using standard algebraic techniques for solving "working together" problems, are fine -- except the one with the arithmetic error!

But the numbers in this problem make a quick informal solution easy, and faster than the formal algebraic solution.

The time working together, 5 1/3 hours, is exactly one-third of the time for Steven working alone.

That means working together is like having three Stevens working; and that means Peter is like two Stevens.

Since Peter is like two Stevens, he can do the job alone in half the time it takes Steven alone.

ANSWER: half of 16 hours, which is 8 hours.