Question

Milena and Mashuka, working together, can complete ajob in 9 days. However, Mashuka works alone and leaves after completing two-fifths of the job. Then Milena takes over and completes the remaining work by herself. As a result the duo could complete the job in 19.5 days. How many days would Milena alone have taken to do the job if Mashuka worked faster than Milena?​

Answer 1

Milena alone would have taken 15 days to do the job

Step-by-step explanation:

Let Milena can complete a job in x days and Mashuka can complete the job in y days

Work done by Milena in 1 day = 1/x

Work done by Mashuka in 1 day = 1/y

Togather in 1 day Milena and Mashuka can do $\frac{1}{x}+\frac{1}{y}$ job

The both can complete the job together in 9 days

Therefore,

$9(\frac{1}{x}+\frac{1}{y})=1$

$\implies \frac{1}{x}+\frac{1}{y}=\frac{1}{9}$

$\implies x+y=\frac{xy}{9}$  ............. (1)

Let Milena completes 2/5 of work in a days and Mashuka compeltes remaining 1/5 work in b days

Then

$a\times\frac{1}{x}=\frac{2}{5}$

$\implies a=\frac{2x}{5}$

Similarly,

$b=\frac{3y}{5}$

According to the question

$a+b=19.5$

$\implies \frac{2x}{5}+\frac{3y}{5}=19.5$

$\implies 2x+3y=97.5$  ............... (2)

Multiplying eq (1) by 2 and subtracting it from eq (2)

We get

$y=97.5-\frac{2xy}{9}$   ...... (3)

$\implies 9y=877.5-2xy$

$\implies 2x=-9+\frac{877.5}{y}$

$\implies x=-4.5+438.75/y$

Putting the value of x in eq (1)

$9(\frac{438.75}{y}-4.5+y)=(\frac{438.75}{y}-4.5)\times y$

$\implies 3948.75-40.5y+9y^2=438.75y-4.5y^2$

$\implies 13.5y^2-479.25y+3948.75=0$

$\implies y^2-35.5y+292.5=0$

$\implies 2y^2-71y+585=0$

$\implies 2y^2-45y-26y+585=0$

$\implies y(2y-45)-13(2y-45)=0$

$\implies (2y-45)(y-13)=0$

$\implies y=13, \frac{45}{2}$

Putting the value of y in eq (3)

$13=97.5-\frac{2x\times 13}{9}$

$\implies 26x=760.5$

$\implies x=29.25$

But it is given that Mashuka works faster than Milena

Therefore, taking $y=45/2=22.5$ and putting it in eq (3)

$22.5=97.5-\frac{2x(22.5)}{9}$

$\implies 45x=75\times 9$

$\implies x=15$

Therefore, Milena alone would have completed the job in 15 days.

Hope this answer was helpful.

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Answer 2

Answer:

Step-by-step explanation: