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It takes two hours for a person $X$ to mow the lawn. $Y$ can mow the same lawn in four hours. How long (in minutes) will it take $X$ and $Y,$ if they work together to mow the lawn$?$

  1. $60$
  2. $80$
  3. $90$
  4. $120$ 
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Migrated from GO Electrical 4 years ago by Arjun

3 Answers

Best answer
3 votes
3 votes
Speed of $X = \frac{1}{2},$ where the unit is number of times lawn is mowed in an hour.
Speed of $Y = \frac{1}{4}$

Effective speed of $X+Y = \frac{1}{2}+\frac{1}{4} = \frac{3}{4}.$

So, time for both $X$ and $Y$ to mow the lawn $ = \frac{1}{\frac{3}{4}} = \frac{4}{3} \text{ hours} = 80 \text{ minutes}$

Correct Answer: Option B.
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X takes $2$ hours to mow the lawn

$\Rightarrow$ In $1$ hour he can mow $\frac{1}{2}$ of the lawn.

Y takes $4$ hours to mow the lawn

$\Rightarrow$ In $1$ hour he can mow $\frac{1}{4}$ of the lawn.

So in $1$ hr X and Y together can mow $\frac{1}{2}$+$\frac{1}{4}$ = $\frac{2+1}{4}$=$\frac{3}{4}$ of the lawn.


X and Y together can mow $\frac{3}{4}$ of the lawn in $1$ hour

$\Rightarrow$ X and Y together can mow $1$ lawn in $1* \frac{4}{3}$ hour = $60* \frac{4}{3}$ = $80$ minutes.

So Option B $80$ is the right answer.

2 votes
2 votes

$Let\ W=4\ unit$

$X\rightarrow2H-\ \ 2unit/H$

$Y\rightarrow4H-\ \ \underline{1unit/H}$

                    $3unit/H$                   

$1H\rightarrow 3unit$

$?\rightarrow 4unit$

$?=\dfrac{4}{3}H=\dfrac{4}{3}\times 60\ min=80\ min$

Answer:

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