In the same period of time that a sports car traveled 120 miles, a truck traveled 100 miles. What was...

Understanding the Question

We need to find the truck's average speed during a journey where:

• Sports car traveled 120 miles
• Truck traveled 100 miles
• Both vehicles traveled for the same time period

Since average speed = \(\mathrm{distance} \div \mathrm{time}\), and we know the truck's distance (100 miles), we need to determine the time period to calculate the truck's speed.

Here's the key insight: When two objects travel for the same time, their speeds are proportional to their distances. Since the truck traveled 100 miles while the sports car traveled 120 miles in the same time period, the truck's speed must be \(\frac{100}{120} = \frac{5}{6}\) of the sports car's speed.

To have sufficiency, we need information that allows us to determine either:

• The actual time period of travel, OR
• A relationship that uniquely determines the truck's speed

Analyzing Statement 1

Statement 1: During the first 30 minutes, the sports car traveled 30 miles.

This tells us the sports car's speed during the first 30 minutes: \(30 \text{ miles} \div 0.5 \text{ hours} = 60 \text{ mph}\).

However, this is only the speed for the FIRST 30 minutes, not the average speed for the entire 120-mile journey. The sports car could have:

• Maintained 60 mph throughout (which would mean completing 120 miles in exactly 2 hours)
• Sped up after 30 minutes (finishing in less than 2 hours total)
• Slowed down after 30 minutes (finishing in more than 2 hours total)

Without knowing the sports car's average speed for the full journey or the total time, we cannot determine the truck's average speed.

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 analyze Statement 2 independently.

Statement 2: The truck's average speed was 10 miles per hour less than the sports car's.

We already established that the truck's speed = \(\frac{5}{6} \times \text{sports car's speed}\) (from the distance ratio).

Statement 2 gives us a second relationship: truck's speed = sports car's speed - 10

These two relationships must be simultaneously true:

• \(\frac{5}{6} \times \text{sports car's speed} = \text{sports car's speed} - 10\)

Let's solve this step by step:

• Sports car's speed - \(\frac{5}{6} \times \text{sports car's speed} = 10\)
• \(\frac{1}{6} \times \text{sports car's speed} = 10\)
• Sports car's speed = 60 mph

Therefore: truck's speed = \(60 - 10 = 50 \text{ mph}\)

We can verify: The truck traveling 100 miles at 50 mph takes 2 hours. The sports car traveling 120 miles at 60 mph also takes 2 hours. ✓

Statement 2 is sufficient. [STOP - Sufficient!]

This eliminates choices C and E.

The Answer: B

Statement 2 alone provides sufficient information to determine the truck's average speed (50 mph), while Statement 1 alone does not.

Answer Choice B: "Statement 2 alone is sufficient, but Statement 1 alone is not sufficient."