P, Q, R and S are four places. To travel from P to R, one travels via Q and to travel from P to S, one travels via both Q and R. Between P and Q, there are 3 routes; between Q and R, there are 4 routes; and between R and S, there are 5 routes. The time taken to travel through these routes is exhibited on the following chart in hours for a specific vehicle: Route times in hours (as per the official solution's chart): Between P and Q: 2, 3, 4. Between Q and R: 1, 1.5, 2, 2. Between R and S: 2, 2, 2.5, 3, 3.5.
How many possible routes are there if the journey takes exactly 7 hours?
- A10
- B11
- C12
- D13
Explanation
Enumerating by the P–Q leg: P–Q = 2 needs Q–R + R–S = 5, giving 3 route combinations; P–Q = 3 needs 4, giving 6 combinations; P–Q = 4 needs 3, giving 2 combinations (using the chart times 2,3,4 / 1,1.5,2,2 / 2,2,2.5,3,3.5 and counting duplicate-time routes separately). The total is 3 + 6 + 2 = 11 routes of exactly 7 hours. Hence option B is correct.