SOLUTION: If it takes Luke 3 hours to rake a yard, and Don 5 hours to rake the same yard, how long will it take them to rake the yard together

Algebra ->  Rate-of-work-word-problems -> SOLUTION: If it takes Luke 3 hours to rake a yard, and Don 5 hours to rake the same yard, how long will it take them to rake the yard together      Log On


   

Question 356789: If it takes Luke 3 hours to rake a yard, and Don 5 hours to rake the same yard, how long will it take them to rake the yard together
Found 2 solutions by Fombitz, Edwin McCravy:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rate*Time=Output
.
.
.
Let Y be the output required to rake the entire yard.
Find each person's rate.
.
.
Luke:
R%5BL%5D%2A3=Y
R%5BL%5D=Y%2F3
.
.
Don:
R%5BD%5D%2A5=Y
R%5BD%5D=Y%2F5
.
.
Luke and Don together:
%28R%5BL%5D%2BR%5BD%5D%29%2At=Y
%28Y%2F3%2BY%2F5%29%2At=Y
%285%2F15%2B3%2F15%29%2At=1
%288%2F15%29%2At=1
highlight%28t=15%2F8%29hours

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
If it takes Luke 3 hours to rake a yard, and Don 5 hours to rake the same yard, how long will it take them to rake the yard together.
First we do it in our head.  Take everything to 15 hours, the LCM of 3 hours and
and 5 hours.  Since Luke can rake 1 yard in 3 hours, he can therefore rake 5
yards in 15 hours.  Similarly since Don can rake 1 yard in 5 hours, he can
therefore rake 3 yards in 15 hours.  So that's 5 yards plus 3 yards they can
rake in working simultaneously for 15 hours, therefore they rake 8 yards in 15
hours or 1 yard in 15%2F8ths of an hour.  That's 1%267%2F8ths hours.

By algebra.  Make this chart:


       Yards raked      Hours      Rate in yards/hr
Luke          1           3              1/3  
Don           1           5              1/5
Together      1           x              1/x

Luke's rate + Don's rate = their rate together
      1/3   +      1/5   =        1/x

Solve that by clearing of fractions and you'll get the same answer as
when we do it in our head.

Edwin