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Question 177698: I would appreciate any help on this problem, I've worked the word problem out from what examples were given in class but the answer I come out with doesn't seem correct when I check it. Please help with this problem:
"Sami and Marisol can mow the lawn in 40 minutes if they work together. If Marisol works twice as fast as Sami, how long does it take Sami to mow the lawn alone?"
Found 3 solutions by stanbon, ankor@dixie-net.com, gonzo:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Sami and Marisol can mow the lawn in 40 minutes if they work together. If Marisol works twice as fast as Sami, how long does it take Sami to mow the lawn alone.
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Together DATA:
time = 40 min/job ; rate = 1/40 job/min
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Sami DATA:
time = 2x min/job ; rate = 1/2x job/min
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Marisol DATA:
time = x min/job ; rate = 1/x job/min
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Rate Equation:
rate + rate = together rate
1/x + 1/2x = 1/40
3x/2x^2 = 1/40
2x^2 = 120x
Divide thru by 2x to get:
x = 60 min (time it takes Marisol to do the job alone)
2x = 120 min (time it takes Sami to do the job alone)
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Cheers,
Stan H.
Answer by ankor@dixie-net.com(22740)  (Show Source):
Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website! the relationship you are looking for is:
rate in number of units per minute * time in minutes = number of units
the number of units is equal to 1 (the lawn).
let the rate of sami in units per minute = x
let the rate of marisol in units per minute = y
formula becomes:
(x + y) * time = 1
time = 40 minutes, so the formula becomes:
(x + y) * 40 = 1
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the problem states that marisol works twice as fast as sami.
that means that marisol can produce twice as many units per minute as sami.
marisol's rate is y
sami's rate = x
marisol's rate being twice as fast as sami's rate means that:
y = 2*x
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they want to know how long it takes sami to mow the lawn alone.
to find that, we need to find sami's rate.
to find sami's rate we need to find either sami's or marisol's rate and, from that, we can find the other.
since we know that y = 2*x, we can susbtitute in the original equation of:
(x + y) * 40 = 1
to get:
(x + 2*x) * 40 = 1
which becomes:
3*x * 40 = 1
dividing both sides of this equation by 120 we get:
x = 1/120
since x is sami's rate, this means that sami can finish 1/120 of the lawn in 1 minute.
since marisol works twice as fast as sami, this means that marisol can finish 2/120 of the lawn in 1 minute.
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let's see if these values hold.
the original equation satates that:
(x + y) * 40 = 1
replace x and y with their respective values to get:
(1/120 + 2/120) * 40 = 1
this becomes:
3/120 * 40 = 1
which becomes:
120/120 = 1
which becomes:
1 = 1
values are good.
sami's rate is 1/120 of the lawn in 1 minute
marisol's rater is 2/120 of the lawn in 1 minute.
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how long does it take sami to mow the lawn?
since rate * time = units, we can solve for time.
1/120 * time = 1
time = 1/(1/120) = 120 minutes.
answer is:
it would take sami 120 minutes to mow the lawn alone.
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