One electrician can rewire a home in 15 hours. Her partner can rewire the same home in 9 hours.

Question

How long will it take the two electrician to rewire the home if they work together?

Answer 1

Hi Lynnelle,

 

This should help you. Basically it's the same concept.

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sally can paint a room in 7 hours while it takes steve 8 hours to paint to same room. how long would it take them to paint the room if they worked together

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Let S = Rate of work, D = Room, and T = Time to paint room
Given: Sally's rate of work as Distance  = D
                                                    Speed       (D/7)
and Steve rate of work as      Distance  =   D
                                                     Speed       (D/8)
 
then T = D
             [(D/7) + (D/8)]
 using the LCM CONCEPT:   [(D/7) + (D/8)] = (8D + 7D)
                                                                                (7)(8)
                                                               = 15D
                                                                   56
 
Using eq. above: T = D/ [(D/7) + (D/8)]
then Subst. in denominator: T =   D
                                                         (15D/56)
 
                                            =  56D
                                                15D
                                            =  3.7333hrs
  Therefore:                  Time =  3hrs, 44mins
 
yesterday | Frank C.
 
Comment
Mitiku D.
Arlington, VA
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0 0
Hi Erica,
 
Start with rewriting the speeds. Instead of saying it takes her 7 hours to finish a room, you would say she can paint 1/7 of a room per hour. and he can paint one eighth (1/8) of a room per hour. 
 
Now you write equation for painting one room.
 
try and think of it in terms distance they can travel per UNIT time. That's the whole point of converting to per hour from per room.
 
you should come up with (1/7)room/hour*time + (1/8)room/hour*time = 1 room
 
time = 1/(1/7+1/8) = 3.7333 = 3 hours and (37.333*60/100) minute = 3 hour and 22 minutes
 
yesterday | Mitiku D.
EditComment
Mark M.
Carson, CA
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0 0
In one hour Sally can do 1/7 of the room.
In one hour Steve can to 1/8 of the room.
 
h = number of hours working together.
 
In h hours Sally can do h/7 of the room.
In h hours Steve can do h/8 of the room.
 
Together the do the 1 room.
 
h/7 + h/8 = 1 
8h/56 + 7h/56 = 1
8h + 7h = 56
15h = 56
h ≈ 3.73
 
Working together they paint the room in 3.73 hours.
yesterday | Mark M.