Clark can do a work in 9 days and Nelson in 15 days. If they work on it together for 5 days then the fraction of the work that is left, is _____

Options

A. `1//15`
B. `1//10`
C. `11//15 `
D. `1//9 `

Answer

To solve the problem, we need to determine the fraction of work left after Clark and Nelson work together for 5 days. Here’s the step-by-step solution:

### Step 1: Determine the total work
Clark can complete the work in 9 days, and Nelson can complete it in 15 days. To find the total work, we can take the least common multiple (LCM) of their work durations.

- LCM of 9 and 15 is 45.

### Step 2: Calculate individual work rates
Next, we calculate how much work each person can do in one day.

- Clark's work rate = Total work / Clark's days = 45 / 9 = 5 units of work per day.
- Nelson's work rate = Total work / Nelson's days = 45 / 15 = 3 units of work per day.

### Step 3: Calculate their combined work rate
Now, we can find their combined work rate when they work together.

- Combined work rate = Clark's work rate + Nelson's work rate = 5 + 3 = 8 units of work per day.

### Step 4: Calculate work done in 5 days
Next, we calculate how much work they can complete together in 5 days.

- Work done in 5 days = Combined work rate × Number of days = 8 × 5 = 40 units of work.

### Step 5: Calculate the work left
Now, we find out how much work is left after they have worked together for 5 days.

- Work left = Total work - Work done = 45 - 40 = 5 units of work.

### Step 6: Calculate the fraction of work left
Finally, we need to express the work left as a fraction of the total work.

- Fraction of work left = Work left / Total work = 5 / 45 = 1 / 9.

### Final Answer
The fraction of the work that is left is **1/9**.

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