SOLUTION: Ezra can type a research paper in 8 hours. Micah helped Ezra in typing,and together they finished in 6 hours. How long will take Micah to finish the job if she worked alone??
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Question: EXERCISES SECTION 8 Work Problems Solve each of the following problems using the 5-step procs u 1,3,n 5 1. Alan can type a research paper in 6 hours. With Steve's help, the paper can be typed rocess: 5 in 4 hours. Find how long it takes Steve to type the paper alone. 2. An experienced roofer can roof a house in 26 hours. A beginning roofer needs 39 hours for
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Frank can type a report in 3 hours and James takes 5 hours. How long will it take the two of them typing together?
Explanation:
Rate of work per hour
Let the count of reports be #k# Let the time taken to write 1 report be #t#
Frank #-> 1/3 t_1=k#
James #->1/5t_2=k#
Set the time to be the same for both (say #t_s# )thus we have
#1/3t_s+1/5t_s=k#
Set the count of reports #k=1#
#1/3t_s+1/5t_s=1#
#t_s(1/3+1/5)=1#
#t_s( 5+3)/15=1#
#8/15t_s=1#
Multiply both sides by #15/8#
#[8/15xx15/8]xxt_s=1xx15/8#
Note that #8/15xx15/8=1#
#t_s=15/8 = 1 7/8# hours
#t_s= 1.875# hours
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Converting this to hours and minutes #1 7/8 hours -> 1 hour +[7/8xx60]" minutes" #
#1 hour color(white)(..) 52 1/2" minutes"#
I suspect this is NOT what they are looking for as an answer format.
Let's consider how much of the report can be done by each person in #1# hour.
In #1# hour Frank can complete one third of the report. #(1/3)#
In #1# hour James can complete one fifth of the report. #(1/5)#
So if they are working together, after #1# hour the fraction of the report that has been completed is:
#1/3 +1/5=(5+3)/15 = 8/15# of the report.
To find out how long it will take working at this rate for #1# hour:
#1 div 8/15#
#15/8# hours
#=1 7/8 = 1.875# hours
#= 1# hour and #7/8 xx60# minutes
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