Question

3 max travels by car to see his brother’s family. he drives 216 miles in 4 hours. what is his rate in miles per hour? use a double number line to show your work. suppose he makes two stops of 10 minutes each during his journey. will he be able to reach the town in 4 hours if he keeps the speed the same?

Explanation:

Step1: Recall the formula for rate (speed)

The formula for speed is \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \).

Step2: Identify the given distance and time

The distance Max drives is 216 miles, and the time taken is 4 hours.

Step3: Calculate the speed

Substitute the values into the formula: \( \text{Speed} = \frac{216}{4} = 54 \) miles per hour.

For the second part (checking if he can reach in 4 hours with two 10 - minute stops):

Step1: Calculate total stop time

Each stop is 10 minutes, and there are 2 stops. So total stop time is \( 2\times10 = 20 \) minutes. Convert 20 minutes to hours: \( \frac{20}{60}=\frac{1}{3}\approx0.333 \) hours.

Step2: Calculate total time available for driving

If he wants to reach in 4 hours, the time he can spend driving is \( 4-\frac{1}{3}=\frac{12 - 1}{3}=\frac{11}{3}\approx3.666 \) hours.

Step3: Calculate the distance he can cover in driving time

Using the speed of 54 miles per hour, the distance covered is \( \text{Distance}=\text{Speed}\times\text{Time}=54\times\frac{11}{3}= 54\times\frac{11}{3}=18\times11 = 198 \) miles. But the original distance is 216 miles. Since \( 198<216 \), he will not be able to reach the town in 4 hours if he makes two 10 - minute stops.

Answer:

Max's rate is 54 miles per hour. He will not be able to reach the town in 4 hours if he makes two 10 - minute stops.