A train will travel 300 kilometers at a constant rate. Write an equation that represents the train’s rate in kilometers per hour (r) based on how many hours the trip takes (t). What is the train’s rate if the trip takes 1.5 hours? kilometers per hour
The Correct Answer and Explanation is:
Answer:
The equation that represents the relationship between the train’s rate rrr (in kilometers per hour) and the time ttt (in hours) is:r=300tr = \frac{300}{t}r=t300
If the trip takes 1.5 hours, then:r=3001.5=200 kilometers per hourr = \frac{300}{1.5} = 200 \text{ kilometers per hour}r=1.5300=200 kilometers per hour
Explanation:
To find the rate of travel, the formula used is:Rate=DistanceTime\text{Rate} = \frac{\text{Distance}}{\text{Time}}Rate=TimeDistance
This formula expresses how fast something is moving over a period of time. In this case, a train is traveling a total distance of 300 kilometers at a constant rate. Because the rate is dependent on how long the trip takes, the variable ttt is used to represent time in hours, and the variable rrr is used to represent the rate in kilometers per hour.
By substituting the known distance into the formula, the relationship becomes:r=300tr = \frac{300}{t}r=t300
This equation shows that the rate is found by dividing the total distance (300 kilometers) by the time ttt it takes to travel that distance. The equation can be used to find the train’s speed for any given time.
For example, if the trip takes 1.5 hours, the value of ttt is 1.5. Substituting into the equation:r=3001.5=200r = \frac{300}{1.5} = 200r=1.5300=200
So, the train’s speed is 200 kilometers per hour. This means the train is traveling fast enough to cover 200 kilometers in one hour. This equation is useful in many real-life scenarios where distance and time are known, and speed needs to be calculated. It also helps to understand the inverse relationship: as time increases, the speed decreases for a fixed distance, and vice versa.
