SOLUTION: A man and a boy together can complete a work in 24 days. If for the last 6 days the man alone does the work it is completed in 26 days. How long the boy will take to complete the w

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A man and a boy together can complete a work in 24 days. If for the last 6 days the man alone does the work it is completed in 26 days. How long the boy will take to complete the w      Log On


   

Question 923881: A man and a boy together can complete a work in 24 days. If for the last 6 days the man alone does the work it is completed in 26 days. How long the boy will take to complete the work alone.
Found 3 solutions by josgarithmetic, ankor@dixie-net.com, MathTherapy:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
RATES, JOB/DAY
Boy, 1/x
Man , 1/y
BothTogether, 1/24

The man alone finished part of the job in 6 days.
highlight%28%281%2F24%29t%2B%281%2Fy%2926=1%29
and
highlight%281%2Fx%2B1%2Fy=1%2F24%29;

Still not enough. Three variables but only two equations.
The description part for the last 6 days the man alone does the work it is completed in 26 days. is contradictory. How many days did the man work alone? 6 or 26 ?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A man and a boy together can complete a work in 24 days.
let m = no. of days for the man to do the job alone
let b = no. of days for the boy to do it
let the completed job = 1
then a shared work equation
24%2Fm + 24%2Fb = 1
If for the last 6 days the man alone does the work, it is completed in 26 days.
The boy works only 20 days in this scenario
26%2Fm + 20%2Fb = 1
Use elimination here,multiply the 1st equation by 5, the 2nd equation by 6
Subtract the 1st from the 2nd
156%2Fm + 120%2Fb = 6
120%2Fm + 120%2Fb = 5
------------------------------Subtraction eliminates b, find a
36%2Fm = 1
m = 36 days the man working alone
:
then using the 1st original equation
24%2F36 + 24%2Fb = 1
reduce the fraction
2%2F3 + 24%2Fb = 1
24%2Fb = 1 - 2%2F3
24%2Fb = 1%2F3
Cross multiply
b = 72 days, the boy working alone
:
;
See if that checks out
24%2F36 + 24%2F72 = 1
reduce fractions
2%2F3 + 1%2F3 = 1
24%2F36 + 24%2Fb = 1




Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
A man and a boy together can complete a work in 24 days. If for the last 6 days the man alone does the work it is completed in 26 days. How long the boy will take to complete the work alone.


Based on the explanation, it appears as though the job was completed in a TOTAL of 26 days as opposed to

24 planned days, with the boy and man working 18 days together. Thus, the man seemed to have completed

the remaining 1/4 of work in 8 (26 - 18) days



If all this is true, then:

Time boy takes, alone to do job is: highlight_green%2896%29 days

You can do the check!! 

===================

If you need a complete and detailed solution, let me know!!



Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com.

Further help is available, online or in-person, for a fee, obviously. 



For FREE info and answers to questions about the ASVAB exam, the NYS 3 – 8 city/state wide exams,GENERAL

MATH and HOMEWORK QUESTIONS, or MATH QUESTIONS related to the Regents Integrated Algebra, 

Regents Geometry, Regents Algebra 2/Trigonometry, SHSAT, COOP/HSPT/TACHS, PSAT, SAT, ACT, SSAT/ISEE,

GRE, CLEP, and the TASC/GED, you can visit: http://asvabstudyzone.freeforums.net/.