Question

john can do three times work as much as tom. they together finish a work in 14 days in how many days john can alone do​

Answer 1

John can do the entire work in 56 days alone.

Step-by-step explanation:

Consider the time taken by Tom = x days,

⇒ his one day work = $\frac{1}{x}$

∵ John can do three times work as much as Tom.

So, the time taken by John = 3x days,

⇒ his one day work = $\frac{1}{3x}$

Thus, total one day work = $\frac{1}{x}+\frac{1}{3x}$

$=\frac{3x+x}{3x^2}$

$=\frac{4x}{3x^2}$

$=\frac{4}{3x}$

∴The time taken when they work together = $\frac{1}{\text{Their one day work}}$

$=\frac{1}{\frac{4}{3x}}$

$=\frac{3x}{4}$

According to the question,

$\frac{3x}{4}=14$

$x=\frac{56}{3}$

Hence, time taken by Jonh alone = 3(56/3) = 56 days.

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