A boat takes 7 hours to go from P to R, through a midpoint Q, but it takes 8 hours to go from P to Q and then return from Q to P. How long it would take to go from R to P?

Options

A. 7 h
B. 8 h
C. 9 h
D. none of these

Answer

To solve the problem step by step, we need to analyze the information given in the question:

1. **Understanding the Journey from P to R**:
- The boat takes 7 hours to travel from point P to point R, passing through a midpoint Q.

2. **Understanding the Journey from P to Q and Back to P**:
- The boat takes 8 hours to go from P to Q and then return from Q to P.

3. **Finding the Time from P to Q**:
- Since Q is the midpoint between P and R, we can assume that the time taken from P to Q is half of the total time taken from P to R.
- Therefore, the time taken from P to Q is:
\[ \text{Time from P to Q} = \frac{7 \text{ hours}}{2} = 3.5 \text{ hours} \]

4. **Finding the Time from Q to P**:
- We know that the total time taken to go from P to Q and back to P is 8 hours.
- We already calculated the time from P to Q as 3.5 hours.
- Let \( t \) be the time taken to go from Q to P. Then:
\[ 3.5 + t = 8 \]
- Solving for \( t \):
\[ t = 8 - 3.5 = 4.5 \text{ hours} \]
- Thus, the time taken from Q to P is 4.5 hours.

5. **Finding the Time from R to P**:
- Since Q is the midpoint, the time taken to go from R to Q should be equal to the time taken to go from P to Q, which is 3.5 hours.
- Therefore, the total time taken to go from R to P is:
\[ \text{Time from R to P} = \text{Time from R to Q} + \text{Time from Q to P} \]
- Substituting the values:
\[ \text{Time from R to P} = 3.5 + 4.5 = 8 \text{ hours} \]

Thus, the time it would take to go from R to P is **8 hours**.