Sure, let’s solve this problem step by step.
Raju finishes [tex]\(\frac{1}{4}\)[/tex] part of the work in 1 hour. We need to find out how much part of the work he will finish in [tex]\(3 \frac{1}{5}\)[/tex] hours.
1. Understand the task: Raju finishes [tex]\(\frac{1}{4}\)[/tex] part of the work in 1 hour. So the first step is to express [tex]\(3 \frac{1}{5}\)[/tex] hours as an improper fraction.
2. Convert mixed number to an improper fraction:
- [tex]\(3 \frac{1}{5}\)[/tex] can be converted by:
[tex]\[
3 \frac{1}{5} = 3 + \frac{1}{5} = \frac{15}{5} + \frac{1}{5} = \frac{16}{5}
\][/tex]
So, [tex]\(3 \frac{1}{5}\)[/tex] hours is [tex]\(\frac{16}{5}\)[/tex] hours.
3. Relate time to work done:
- Since Raju completes [tex]\(\frac{1}{4}\)[/tex] of the work in 1 hour, he completes [tex]\(\frac{1}{4} \times \frac{16}{5}\)[/tex] of the work in [tex]\( \frac{16}{5} \)[/tex] hours.
4. Multiply to find the work done:
[tex]\[
\frac{1}{4} \times \frac{16}{5} = \frac{16}{4 \times 5} = \frac{16}{20} = \frac{4}{5}
\][/tex]
So, in [tex]\(3 \frac{1}{5}\)[/tex] hours, Raju will have finished [tex]\(\frac{4}{5}\)[/tex] or [tex]\(0.8\)[/tex] part of the work.
