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Deconstructing the Question
The problem asks for the time difference between Tom and John covering the same distance (from the passing point to the Gas Station).
Since the Distance is constant, we can use the Ratio Method instead of calculating specific distances.
Step 1: Determine the Ratios
Calculate the ratio of their speeds:
\(\frac{S_T}{S_J} = \frac{15}{10} = \frac{3}{2}\)
Since Speed and Time are inversely proportional for a constant distance:
\(\frac{t_J}{t_T} = \frac{3}{2}\) (John takes 3 units of time for every 2 units Tom takes).
Step 2: Calculate John's Total Time
We know Tom takes 15 minutes. Let's solve for John's time (\(t_J\)):
\(t_J = t_T \times \frac{3}{2}\)
\(t_J = 15 \times 1.5 = 22.5 \text{ minutes}\)
Step 3: Interpret the Question Context
The calculated total time for John is 22.5 minutes. Looking at the options (5, 6, 7.5...), none match the total time.
The question phrasing implies: "How many more minutes does it take John to arrive after Tom has arrived?"
\(\text{Time Difference} = t_J - t_T\)
\(\text{Time Difference} = 22.5 - 15 = 7.5 \text{ minutes}\)
This matches option C perfectly.
Answer: C
The problem asks for the time difference between Tom and John covering the same distance (from the passing point to the Gas Station).
Since the Distance is constant, we can use the Ratio Method instead of calculating specific distances.
- Tom's Speed (\(S_T\)): 15 km/h
- John's Speed (\(S_J\)): 10 km/h
- Tom's Time (\(t_T\)): 15 minutes
Step 1: Determine the Ratios
Calculate the ratio of their speeds:
\(\frac{S_T}{S_J} = \frac{15}{10} = \frac{3}{2}\)
Since Speed and Time are inversely proportional for a constant distance:
\(\frac{t_J}{t_T} = \frac{3}{2}\) (John takes 3 units of time for every 2 units Tom takes).
Step 2: Calculate John's Total Time
We know Tom takes 15 minutes. Let's solve for John's time (\(t_J\)):
\(t_J = t_T \times \frac{3}{2}\)
\(t_J = 15 \times 1.5 = 22.5 \text{ minutes}\)
Step 3: Interpret the Question Context
The calculated total time for John is 22.5 minutes. Looking at the options (5, 6, 7.5...), none match the total time.
The question phrasing implies: "How many more minutes does it take John to arrive after Tom has arrived?"
\(\text{Time Difference} = t_J - t_T\)
\(\text{Time Difference} = 22.5 - 15 = 7.5 \text{ minutes}\)
This matches option C perfectly.
Answer: C
