Questions: Question 10 (Mandatory) (1 point) A car and a bus set out at 4 P.M. from the same point headed in the same direction. The average speed of the car is twice the average speed of the bus. In 2 h , the car is 68 mi ahead of the bus. Find the rate of the car. 68 mph 58 mph 65 mph 55 mph

Question 10 (Mandatory) (1 point) A car and a bus set out at 4 P.M. from the same point headed in the same direction. The average speed of the car is twice the average speed of the bus. In 2 h , the car is 68 mi ahead of the bus. Find the rate of the car. 68 mph 58 mph 65 mph 55 mph
Transcript text: Question 10 (Mandatory) (1 point) A car and a bus set out at 4 P.M. from the same point headed in the same direction. The average speed of the car is twice the average speed of the bus. In 2 h , the car is 68 mi ahead of the bus. Find the rate of the car. 68 mph 58 mph 65 mph 55 mph
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Solution

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Solution Steps

To find the rate of the car, we need to set up an equation based on the information given. Let the speed of the bus be \( x \) mph. Then, the speed of the car is \( 2x \) mph. In 2 hours, the car travels \( 2 \times 2x = 4x \) miles, and the bus travels \( 2 \times x = 2x \) miles. The difference in distance traveled by the car and the bus is 68 miles. Therefore, we can set up the equation \( 4x - 2x = 68 \) and solve for \( x \). Once we find \( x \), we can determine the rate of the car, which is \( 2x \).

Step 1: Define Variables and Relationships

Let the speed of the bus be \( x \) mph. According to the problem, the speed of the car is twice the speed of the bus, so the speed of the car is \( 2x \) mph.

Step 2: Set Up the Equation

In 2 hours, the car travels \( 2 \times 2x = 4x \) miles, and the bus travels \( 2 \times x = 2x \) miles. The car is 68 miles ahead of the bus, so we can set up the equation: \[ 4x - 2x = 68 \]

Step 3: Solve for \( x \)

Simplify the equation: \[ 2x = 68 \] Divide both sides by 2 to solve for \( x \): \[ x = \frac{68}{2} = 34 \]

Step 4: Calculate the Rate of the Car

The rate of the car is \( 2x \). Substitute \( x = 34 \) into the expression for the car's speed: \[ 2x = 2 \times 34 = 68 \]

Final Answer

The rate of the car is \(\boxed{68 \text{ mph}}\).

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