Working 5 hours a day. A can complete a work in 8 days and working 6 hours a day, B can complete the same work in 10 days. Working 8 hours a day, they can jointly complete the work in

Options

A. 3 days
B. 4 days
C. 4.5 days
D. 5.4 days

Answer

To solve the problem step by step, we need to determine how long A and B will take to complete the work when they work together for 8 hours a day.

### Step 1: Calculate the total work done by A and B

1. **Calculate A's work rate:**
- A can complete the work in 8 days, working 5 hours a day.
- Total hours A works = 8 days × 5 hours/day = 40 hours.
- Therefore, A's work rate = Total work / Total hours = 1 work unit / 40 hours = 1/40 work units per hour.

2. **Calculate B's work rate:**
- B can complete the work in 10 days, working 6 hours a day.
- Total hours B works = 10 days × 6 hours/day = 60 hours.
- Therefore, B's work rate = Total work / Total hours = 1 work unit / 60 hours = 1/60 work units per hour.

### Step 2: Combine the work rates of A and B

3. **Calculate their combined work rate:**
- Combined work rate = A's work rate + B's work rate
- Combined work rate = (1/40 + 1/60) work units per hour.

4. **Finding a common denominator:**
- The least common multiple (LCM) of 40 and 60 is 120.
- Convert the fractions:
- (1/40) = (3/120)
- (1/60) = (2/120)
- Therefore, combined work rate = (3/120 + 2/120) = (5/120) = (1/24) work units per hour.

### Step 3: Calculate the time taken to complete the work together

5. **Calculate the time taken to complete the work together:**
- If A and B work together, they complete 1/24 of the work in 1 hour.
- To complete 1 work unit, the time taken = 1 work unit / (1/24 work units per hour) = 24 hours.

### Step 4: Calculate how many days they will take working 8 hours a day

6. **Calculate the number of days required:**
- If they work 8 hours a day, the number of days required = Total hours / Hours per day = 24 hours / 8 hours/day = 3 days.

### Final Answer:
A and B can jointly complete the work in **3 days** when working 8 hours a day.

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