Two cars raced at a race track. The faster car traveled 20 mph faster than the slower car. In the time that the slower car traveled 165 miles, the faster car traveled 225 miles. If the speeds of the cars remained constant, how fast did the slower car travel during the race?
| | Distance (mi) | Rate (mph) | Time (h) |
| :------------ | :------------ | :--------- | :---------- |
| Slower Car | 165 | $r$ | $\frac{165}{r}$ |
| Faster Car | 225 | $r+20$ | $\frac{225}{r+20}$ |
A. 55 mph
B. 60 mph
C. 75 mph
D. 130 mph
Answer (2)
Define the variable: Let r be the speed of the slower car.
Set up the equation: r 165 = r + 20 225 .
Solve for r : 165 ( r + 20 ) = 225 r ⇒ 165 r + 3300 = 225 r ⇒ 60 r = 3300 ⇒ r = 55 .
State the final answer: The speed of the slower car is 55 mph.
Explanation
Problem Analysis Let's analyze the problem. We are given that the faster car travels 20 mph faster than the slower car. We also know that the slower car travels 165 miles in the same time that the faster car travels 225 miles. Our goal is to find the speed of the slower car.
Setting up the Equation Let r be the speed of the slower car in mph. Then the speed of the faster car is r + 20 mph. The time it took the slower car to travel 165 miles is r 165 hours. The time it took the faster car to travel 225 miles is r + 20 225 hours. Since these times are equal, we can set up the equation: r 165 = r + 20 225
Solving the Equation To solve the equation, we cross-multiply: 165 ( r + 20 ) = 225 r Expanding the left side, we get: 165 r + 165 ( 20 ) = 225 r 165 r + 3300 = 225 r
Finding the Speed of the Slower Car Now, we want to isolate r . Subtract 165 r from both sides: 3300 = 225 r − 165 r 3300 = 60 r Divide both sides by 60: r = 60 3300 r = 55
Final Answer Therefore, the speed of the slower car is 55 mph.
Examples
Imagine two athletes running a race. One is consistently faster but starts a bit later. This problem helps determine the speed of the slower runner, given the distance each covers in the same amount of time and the speed difference. Understanding relative speeds and distances is crucial in various real-life scenarios, such as planning travel times, coordinating logistics, or even understanding competitive performance in sports.
The speed of the slower car is calculated to be 55 mph. This is determined by analyzing the distances each car traveled in the same time and setting up an equation based on their speeds. After solving the equation, we find that the slower car's speed is 55 mph.
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