Which equation represents the distance $(d)$ a car travels, in time $(t)$, when driving 65 miles per hour? How far did the car travel in 3 hours?
A) $d=65 t, 21.7$ miles
B) $d=65 t, 195$ miles
C) $t=65 d ; 21.7$ hours
D) $t=65 d ; 195$ hours
Answer (1)
The problem provides the speed of a car and asks for the distance it travels in a given time.
The formula d = v \t relates distance, speed, and time.
Substitute the given speed v = 65 mph into the formula to get d = 65 t .
Calculate the distance traveled in 3 hours by substituting t = 3 into the equation: d = 65 \t 3 = 195 miles. Therefore, the final answer is 195 miles .
Explanation
Understanding the Problem We are given that a car is traveling at a constant speed of 65 miles per hour. We want to find the equation that relates the distance, d , the car travels in a given amount of time, t . We also want to find the distance the car travels in 3 hours.
Distance, Speed, and Time The formula relating distance, speed, and time is: d = v \t where:
d is the distance traveled,
v is the speed,
t is the time.
Finding the Equation In this problem, the speed v is given as 65 miles per hour. Substituting this value into the formula, we get: d = 65 t
Calculating the Distance Now we want to find the distance the car travels in 3 hours. We substitute t = 3 into the equation: d = 65 \t = 65 \t 3 = 195 So, the car travels 195 miles in 3 hours.
Choosing the Correct Option Comparing our results with the given options, we see that option B matches our equation and calculated distance.
Final Answer Therefore, the equation that represents the distance the car travels is d = 65 t , and the car travels 195 miles in 3 hours.
Examples
Understanding the relationship between distance, speed, and time is crucial in many real-life scenarios. For example, if you're planning a road trip, knowing your average speed and the time you'll be driving allows you to estimate the total distance you'll cover. Similarly, if you know the distance you need to travel and the time you have, you can calculate the required speed to reach your destination on time. This concept is also used in logistics and transportation to optimize delivery routes and schedules. The formula d = v \t is a fundamental tool for solving these types of problems.
For instance, imagine you are driving at a constant speed of 60 miles per hour for 2.5 hours. Using the formula, you can calculate the distance covered as follows: d = 60 \t 2.5 = 150 So, you would have traveled 150 miles.
