Question

Dorji take double the time than dawa to dig a garden. If dawa takes 2 hours 30 minutes to dig the garden alone, how long will it take to dig the garden together

Answer 1

Given:

Dorji takes double the time than Dawa to dig a garden.

If Dawa takes 2 hours 30 minutes to dig the garden alone

To find:

How long will it take to dig the garden together?

Solution:

We are given that Dorji takes twice the time than Dawa to dig a garden and we have

Dawa can dig a garden in = 2 hrs 30 min = $2\frac{30}{60} = 2\frac{1}{2} = \frac{5}{2}\:hrs$

∴ To dig the same garden, Dorji will take = $2\times \frac{5}{2} = 5\:hrs$

So, we can say that

In 1 hr, Dawa will dig = $\frac{1}{\frac{5}{2} } = \frac{2}{5} \:of \:the\:garden$

and

In 1 hr, Dorji will dig = $\frac{1}{5} \:of \:the\:garden$

Now,

In 1 hr, both Dawa and Dorji together will dig,

= $\frac{2}{5} + \frac{1}{5}$

= $\bold{\frac{3}{5} }$

∴ Both Dawa & Dorji will take = $\frac{5}{3} \:hrs = 1 \frac{2}{3} \:hrs = 1\: hr\: 40\: mins$ to dig a garden.

Thus, it will take 1 hr 40 minutes to dig the garden together.

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