A is 4 times than B. if together they can complete a work in 5 days, then in how many days B can complete the same work?

Let the amount of work completed by B in 1 day be \( B \) units. Then, the amount of work completed by A in 1 day is \( 4B \) units (since A is 4 times faster than B).

Together, A and B complete the work in 5 days. Therefore, their combined work rate is:

\[
\text{Work rate of A + Work rate of B} = \frac{1}{5} \, \text{(since they complete the work in 5 days)}.
\]

This means:

\[
4B + B = \frac{1}{5}.
\]

Simplifying:

\[
5B = \frac{1}{5}.
\]

Solving for \( B \):

\[
B = \frac{1}{25}.
\]

Thus, B completes \( \frac{1}{25} \) of the work in 1 day, which means B will take 25 days to complete the work alone.

### Answer: B can complete the work in **25 days**.

Would you like a further breakdown of this solution or to ask related questions?

Here are some related questions:
1. What if A were 3 times as efficient as B instead of 4?
2. How would the solution change if they completed the work together in 6 days?
3. How do we interpret work rates in more complex real-world problems?
4. How can we set up a similar problem where A is slower than B?
5. What if A and B had different work rates that are not multiples of each other?

**Tip:** Always ensure units (like days or work completed per day) are consistent throughout the problem.

A is 4 times than B. If together they can complete a work in 5 days, then in how many days B can complete the same work?

Explore the solution to a work rate problem where A is 4 times faster than B, and they complete a task together in 5 days. Learn how to calculate the time B takes to complete the work alone using algebraic methods. Suitable for Grades 7-9 students.

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