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

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(39617)   (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.

and
;

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)   (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
+ = 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
+ = 1
Use elimination here,multiply the 1st equation by 5, the 2nd equation by 6
Subtract the 1st from the 2nd
+ = 6
+ = 5
------------------------------Subtraction eliminates b, find a
= 1
m = 36 days the man working alone
:
then using the 1st original equation
+ = 1
reduce the fraction
+ = 1
= 1 -
=
Cross multiply
b = 72 days, the boy working alone
:
;
See if that checks out
+ = 1
reduce fractions
+ = 1
+ = 1

Answer by MathTherapy(10552)   (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: 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/.
RELATED QUESTIONS
my question: a man and a boy complete work together in 24 days. if for the last 6 days... (answered by ewatrrr)
if a man completes a work in 9 days,second man complete work in 7 days and 3 mens... (answered by ankor@dixie-net.com)
One man and 2 boys can do a piece of work in 12 days, which can also be done by 3 men and (answered by 303795)
one man & 2 boys can do a piece of workin 12 days, which can also done by 3 men & 1 boy... (answered by stanbon)
if a man and a boy can do a work in 8 days,this work can do 2 man and 4 boy in 3 days... (answered by josmiceli)
Hi, I am having difficulty putting this problem into an equation even though I know the... (answered by ankor@dixie-net.com,scott8148)
A and B can complete a work in 2 and 6 days respectively. If C alone can complete the... (answered by ptaylor)
A,B and C can finish a job in 6 days. If B and C work together, the job will take 9 days; (answered by stanbon,harshachittar)
A and B together can complete a work in 12 days. C alone can complete the same work in... (answered by ikleyn,Theo,greenestamps,math_tutor2020,Edwin McCravy,MathTherapy)