Distance, Rate, and Time

What is the formula that relates distance, rate, and time?

• d = r + t

• d = r - t

• d = r × t

• d = r / t

Answer explanation

The formula that relates distance (d), rate (r), and time (t) is d = r × t. This means distance is equal to the rate of travel multiplied by the time spent traveling.

In the formula d = r × t, what does 'r' represent?

• Distance

• Rate (or speed)

• Time

• Resistance

Answer explanation

In the formula d = r × t, 'r' represents the rate (or speed) at which distance is covered over time. Therefore, the correct answer is 'Rate (or speed)'. This indicates how fast an object is moving.

If Train A travels at 80 km/h and Train B at 100 km/h, what is the combined speed of both trains?

• 180 km/h

• 200 km/h

• 150 km/h

• 160 km/h

Answer explanation

To find the combined speed of Train A and Train B, simply add their speeds: 80 km/h + 100 km/h = 180 km/h. Therefore, the correct answer is 180 km/h.

How can the formula d = r × t be rearranged to solve for time (t)?

• t = d × r

• t = d / r

• t = r / d

• t = r × d

Answer explanation

To solve for time (t) in the formula d = r × t, divide both sides by r. This gives t = d / r, which is the correct rearrangement. The other options do not correctly isolate t.

What is the formula used to calculate distance in the given example?

• d = r + t

• d = r - t

• d = r × t

• d = r / t

Answer explanation

The correct formula to calculate distance is d = r × t, where d is distance, r is rate, and t is time. This formula shows that distance is directly proportional to both rate and time.

How long will it take for the two trains to meet according to the calculation?

• 15 hours

• 20 hours

• 25 hours

• 30 hours

Answer explanation

To find when the two trains meet, we calculate their speeds and distances. Given the data, they will meet in 20 hours, which is the correct answer.

How far will Train A have traveled when the two trains meet?

• 1,200 kilometers

• 1,400 kilometers

• 1,600 kilometers

• 1,800 kilometers

Answer explanation

To find the distance Train A travels when the two trains meet, we can use the relative speeds and the total distance. Given the conditions, Train A will have traveled 1,600 kilometers when they meet.

How far will Train B have traveled when the two trains meet?

• 1,800 kilometers

• 2,000 kilometers

• 2,200 kilometers

• 2,400 kilometers

Answer explanation

To find how far Train B has traveled when the two trains meet, we can use the relative speeds and the time taken. Given the conditions, Train B travels 2,000 kilometers before meeting Train A.

What is one way to deepen your understanding of distance, rate, and time relationships?

• Memorizing formulas

• Varying the parameters of the problem

• Reading more books

• Watching videos

Answer explanation

Varying the parameters of the problem allows you to see how changes in distance, rate, and time affect each other, deepening your understanding of their relationships through practical application.

What effect does increasing the speed of one train have on the time it takes for two trains to meet?

• It increases the time

• It decreases the time

• It has no effect

• It doubles the time

Answer explanation

Increasing the speed of one train reduces the time it takes for the two trains to meet. As one train moves faster, the distance between them closes more quickly, leading to a decrease in meeting time.