Sheldon left his house at 8:30 a.m. and drove to his friend's house, arriving later that morning at 11:30 a.m....

Understanding the Question

We need to find the total distance Sheldon drove from his house to his friend's house.

Given Information

• Departure time: 8:30 a.m.
• Arrival time: 11:30 a.m.
• Total elapsed time: 3 hours

What We Need to Determine

To find distance, we use: \(\mathrm{Distance} = \mathrm{Speed} \times \mathrm{Time}\)

Here's the crucial insight: the 3-hour elapsed time includes both driving time and stopping time. So we actually need:

• \(\mathrm{Distance} = \mathrm{Average\ driving\ speed} \times \mathrm{Actual\ driving\ time}\)

This means we must know both the driving speed AND the actual time spent driving (which equals 3 hours minus total stopping time).

Analyzing Statement 1

Statement 1: He stopped twice along the way.

This tells us about the trip structure, but consider what's still unknown:

• How long was each stop?
• What was his driving speed?
• What was the actual driving time?

Without knowing the duration of the stops, we cannot separate driving time from stopping time. And without knowing either the driving time or the driving speed, we cannot calculate distance.

Statement 1 is NOT sufficient.

[STOP - Not Sufficient!] This eliminates choices A and D.

Analyzing Statement 2

Now let's forget Statement 1 completely and evaluate Statement 2 independently.

Statement 2: His average speed while he was driving was 96 kilometers per hour.

This gives us the driving speed, but we face a critical problem: we don't know how much of the 3 hours was spent driving versus stopping.

Let's visualize with concrete scenarios:

• Scenario 1: No stops → Drove full 3 hours → Distance = \(96 \times 3 = \) 288 km
• Scenario 2: Stopped for 1 hour total → Drove 2 hours → Distance = \(96 \times 2 = \) 192 km
• Scenario 3: Stopped for 30 minutes total → Drove 2.5 hours → Distance = \(96 \times 2.5 = \) 240 km

Each scenario produces a different distance. Without knowing the stopping time, we cannot determine a unique answer.

Statement 2 is NOT sufficient.

[STOP - Not Sufficient!] This eliminates choice B.

Combining Both Statements

Using both statements together, we know:

• From Statement 1: He made two stops
• From Statement 2: His driving speed was 96 km/hr
• From the question: Total elapsed time was 3 hours

But here's the key: even with both pieces of information, we still don't know the duration of the two stops. Consider these possibilities:

• Two 5-minute breaks: Total stop time = 10 minutes = 1/6 hour
  • Driving time = 3 - 1/6 = 2.83 hours
  • Distance = \(96 \times 2.83 \approx \) 272 km

• Two 30-minute breaks: Total stop time = 1 hour
  • Driving time = 3 - 1 = 2 hours
  • Distance = \(96 \times 2 = \) 192 km

• One 10-minute and one 50-minute break: Total stop time = 1 hour
  • Driving time = 3 - 1 = 2 hours
  • Distance = \(96 \times 2 = \) 192 km

Different stop durations → Different driving times → Different distances

We still cannot determine a unique answer.

Both statements together are NOT sufficient.

[STOP - Not Sufficient!] This eliminates choice C.

The Answer: E

Since:

• Statement 1 alone is NOT sufficient
• Statement 2 alone is NOT sufficient
• Both statements together are NOT sufficient

The answer is E: The statements together are not sufficient.