Question

A train traveled 3/4 of the distance between two cities in 1/2 of an hour. How long does it take the train to travel the full distance?

A) 30 minutes
B) 40 minutes
C) 45 minutes
D) 60 minutes

Answer 1

The train takes 1 hour to travel the full distance between the two cities. Thus the correct answer is D).

Step-by-step explanation:

Given that the train traveled 3/4 of the distance in 1/2 of an hour, we can determine its speed. Using the formula speed = distance / time, the train's speed can be calculated as 3/4 divided by 1/2, which equals 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2 of the full distance per hour. Therefore, to cover the entire distance, which represents 1 whole unit, it will take the train 1 hour, as the rate of travel remains constant.

Initially, we know the train traveled 3/4 of the distance in 1/2 of an hour, implying it covers 3/4 of the distance in half the time it would take to cover the entire distance. Using the relationship between the time taken and the proportion of distance covered, we can determine the train's constant speed. As the train covers 3/4 of the distance in 1/2 hour, it maintains this speed to cover the full distance, which, based on the rate calculated, is 1 unit in 1 hour.

Understanding the relationship between the portion of the distance covered and the time taken helps in computing the constant speed at which the train is traveling. In this scenario, applying the ratio of the distance covered to the time taken allows us to establish the rate of travel, which, when extended to cover the full distance, indicates that the train will take 1 hour to complete the entire journey between the two cities.Thus the correct answer is D).

Answer 2

The train takes 40 minutes to travel the full distance between two cities, as it travels 3/4 of that distance in 1/2 hour.

Step-by-step explanation:

The student asked, 'A train traveled 3/4 of the distance between two cities in 1/2 of an hour. How long does it take the train to travel the full distance?' The information given indicates that if 3/4 of the distance is covered in 1/2 hour, then the full distance would take longer than 1/2 hour but less than double that time since we're looking for the full distance, which is 4/4 (or 1).

Using the fact that the train travels 40 miles one way and back, making a total distance of 80 miles, this additional information is provided for context, although it does not change the calculation for our original question.

To find the time for the full distance, we need to consider the proportion of time it takes to travel the given part of the trip: 3/4 of the distance takes 1/2 hour, so 1/4 of the distance takes 1/2 divided by 3, which is 1/6 hour. Therefore, the full distance (4/4) would take (1/6) × 4, which is 2/3 of an hour. Since 1 hour is 60 minutes, 2/3 hour is the same as 40 minutes. Therefore, the correct answer is B) 40 minutes.