Question

Bob can finish a job in 40 days,if he works alone. Alex is twice as fast as Bob and thrice as fast as Cole in the same job.Suppose Alex and Bob work together on the first day,Bob and Cole work together on the second day,Cole and Alex work together on the third day and then,they continue the work by repeating this three-day roster,with Alex and Bob working together on the fourth day and so on.Then,the total number of days Alex would have worked when the job gets finished,is

Answer 1

Correct Answer: 11

We are given that Bob, Alex, and Cole have different daily productivity rates, and they work together to complete a task. Let's define their productivity:

• Bob: 3 units/day
• Alex: 6 units/day
• Cole: 2 units/day

Step 1: Calculate the total amount of work

Bob can complete the task in 40 days. Therefore, the total work is: \[ 40 \times 3 = 120 \text{ units}. \]

Step 2: Work completed in the first three days

On the first day, Bob and Alex work together. They complete: \[ 3 + 6 = 9 \text{ units}. \] On the second day, Bob and Cole work together. They complete: \[ 3 + 2 = 5 \text{ units}. \] On the third day, Alex and Cole work together. They complete: \[ 6 + 2 = 8 \text{ units}. \] So, the total work completed in the first three days is: \[ 9 + 5 + 8 = 22 \text{ units}. \]

Step 3: Work completed in the first 15 days

In the first 15 days, the total work completed is: \[ 22 \times 5 = 110 \text{ units}. \] This leaves 10 units remaining, which can be completed in 2 more days.

Step 4: Determine Alex’s working days

Since Alex works 2 out of every 3 days, he will work for: \[ 10 \text{ days in the first 15 days}. \] Additionally, Alex will work on the 16th day to complete the task. Therefore, Alex works a total of: \[ 10 + 1 = 11 \text{ days}. \]

Final Answer:

The total number of days Alex works is \( \boxed{11} \) days.