Question

traveling at an average rate of between 50 and 60 miles per hour for 4 to 5 hours, select the best estimate for the distance traveled.
150 miles 255 miles 280 miles 295 miles
choose the best estimate for the distance traveled.
a. 255 miles b. 150 miles
c. 280 miles d. 295 miles

Explanation:

Step1: Recall distance formula

The formula for distance is \( \text{Distance} = \text{Rate} \times \text{Time} \).

Step2: Find minimum and maximum distance

• Minimum distance: Rate = 50 mph, Time = 4 hours. So \( 50 \times 4 = 200 \) miles.
• Maximum distance: Rate = 60 mph, Time = 5 hours. So \( 60 \times 5 = 300 \) miles.

Step3: Analyze options

• Option B (150 miles) is less than 200, invalid.
• Option A (256 miles): Check if within 200 - 300. 256 is in range.
• Option C (280 miles): In range, but let's check average rate and time.
• Option D (295 miles): Close to 300, but let's see average.

Average rate: \( \frac{50 + 60}{2} = 55 \) mph. Average time: \( \frac{4 + 5}{2} = 4.5 \) hours. Distance: \( 55 \times 4.5 = 247.5 \), close to 256 (255 is given, 256 is option A). 280 and 295 are higher than average estimate. So 256 is a better estimate.

Answer:

A. 256 miles