Question

Sofia can type the work in 10 hours. Nova can do it in 15 hours. They work together for 4 hours, then Sofia and Nova finish the job. How long did it take to do the entire job?

Answer 1

Answer:

2 days.

Step-by-step explanation:

Let, Sofia can type the x amount of work in 10 hours.

So, in one hour Sofia can type $\frac{x}{10}$ amount of work.

Again, Nova can type x amount of work in 15 hours.

So, in one hour Nova can type $\frac{x}{15}$ amount of work.

Hence, if they work together, they can type $\frac{x}{10} + \frac{x}{15} = \frac{6x + 4x}{60} = \frac{10x}{60} = \frac{x}{6}$ amount of work in one hour.

Therefore, working together they can type the x amount of work in $\frac{x}{\frac{x}{6} } = 6$ days.

So, they have to work for (6 - 4) = 2 days more to finish the work. (Answer)

Answer 2

Sofia and Nova together completes the work in 6 hours.

SOLUTION:

Given, Sofia can type the work in 10 hours.  

Nova can do it in 15 hours.  

They work together for 4 hours, then Sofia and Nova finish the job.  

We have to find time taken to do the entire job

Now, work done by Sofia in 1 hour $=\frac{1}{10}$

And work done by Nova in 1 hour $=\frac{1}{15}$

Then, when they are together, work done in 1 hour $=\frac{1}{10}+\frac{1}{15}=\frac{1}{5}\left(\frac{1}{2}+\frac{1}{3}\right)=\frac{1}{5}\left(\frac{3+2}{6}\right)=\frac{1}{5} \times \frac{5}{6}=\frac{1}{6}$

So, $\text { total required time }=\frac{1}{\frac{1}{6}}=6 \text { hours }$