Question

Vannesa can plough a garden in 24 hours and Austin can do the same job in 36 hours. They work together for 6 hours, then Austin stops working. How long will it take Vannesa to finish the job

Answer 1

Step-by-step explanation:

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Answer 2

Given:

Vannesa can plough a garden in 24 hours

Austin can do the same job in 36 hours.

Vannesa & Austin work together for 6 hours then Austin stops working.

To find:

Time required by Vannesa to finish the job of ploughing the garden

Solution:

So,

The amount of work done by Vannesa in 1 hour = $\frac{1}{24}$

The amount of work done by Austin in 1 hour = $\frac{1}{36}$

The amount of work done by Vannesa & Austin together in 1 hour = $\frac{1}{24} + \frac{1}{36}$

Since they work together for 6 hours

∴ The amount of work done by Vannesa & Austin together in 6 hours,

= $6\times [\frac{1}{24} + \frac{1}{36}]$

= $6\times [\frac{3+2}{72} ]$

= $6 \times [\frac{5}{72} ]$

= $\frac{30}{72}$

= $\frac{5}{12}$

Let "x" hours represent the no. of days Vannesa takes to finish the remaining job.

Now,

According to the question, the equation that will represent the the entire job of ploughing a garden is given as follows:

[Amount of work done by both of them in 6 hours] + [Amount of work done by Vannesa in x hours] = [The whole job of ploughing]

i.e., $\frac{5}{12} \:+\:x[\frac{1}{24}] = 1$

⇒ $\frac{10 \:+\: x}{24} = 1$

⇒ $10\:+\:x = 24$

⇒ $x = 24\: -\: 10$

⇒ $\bold{x = 14 \:hours}$

Thus, Vannesa will take 14 hours to finish the job.

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