If distance = rate x time, which of the following must also be true?

• Rate = distance x time

• Time = distance/rate

• Distance = rate/time

• Time = rate/distance

Answer explanation

From the formula distance = rate x time, we can rearrange it to find time. Dividing both sides by rate gives time = distance/rate, making this the correct choice. The other options do not correctly represent the relationship.

If a train travels at a speed of 100 km/hr, how far will it travel in half an hour?

• 100 km

• 50 km

• 25 km

• 10 km

Answer explanation

To find the distance traveled, use the formula: Distance = Speed × Time. Here, Speed = 100 km/hr and Time = 0.5 hr. Thus, Distance = 100 × 0.5 = 50 km. Therefore, the correct answer is 50 km.

If a jogger runs a 10-kilometer race in 60 minutes, what is her average speed?

• 10 km/hr

• 5 km/hr

• 6 km/hr

• 1.66 km/hr

Answer explanation

To find the average speed, divide the distance by the time. The jogger runs 10 kilometers in 60 minutes, which is 1 hour. Thus, average speed = 10 km / 1 hr = 10 km/hr, making the correct answer 10 km/hr.

If a car travels at 40 km/hr for 4 hours, how much distance has it covered?

• 160 km

• 140 km

• 120 km

• 100 km

Answer explanation

To find the distance covered, use the formula: Distance = Speed × Time. Here, Speed = 40 km/hr and Time = 4 hours. Thus, Distance = 40 × 4 = 160 km. Therefore, the correct answer is 160 km.

An aircraft carrier travels a distance of 1,000 km in 3 days. What is its average rate of speed?

• 1,000 km/hr

• 3,000 km/hr

• 333.3 km/hr

• 13.9 km/hr

Answer explanation

To find the average speed, divide the total distance by the total time. Here, 1,000 km / 72 hours (3 days) = 13.9 km/hr. Thus, the correct answer is 13.9 km/hr.

A train leaves New York traveling at a speed of 90 km/hr. How much distance will it cover in five hours?

• 45 km

• 450 km

• 180 km

• 18 km

Answer explanation

To find the distance covered, use the formula: Distance = Speed × Time. Here, Speed = 90 km/hr and Time = 5 hours. Thus, Distance = 90 km/hr × 5 hr = 450 km. Therefore, the correct answer is 450 km.

If a train travels 1,600 km in 16 hours, how fast is it moving?

• 60 km/hr

• 100 km/hr

• 120 km/hr

• 90 km/hr

Answer explanation

To find the speed, divide the distance by time: 1600 km ÷ 16 hours = 100 km/hr. Therefore, the train is moving at 100 km/hr.

If a person ran 32 kilometers at a rate of 8 kilometers/hr, how long did he run?

• 6 hours

• 8 hours

• 4 hours

• 12 hours

Answer explanation

To find the time taken, use the formula: time = distance / speed. Here, time = 32 km / 8 km/hr = 4 hours. Thus, the correct answer is 4 hours.

A crosstown bus travels 8 kilometers in 45 minutes. What is its average rate of speed?

• 4 km/hr

• 6.67 km/hr

• 8 km/hr

• 10.67 km/hr

Answer explanation

To find the average speed, divide the distance by the time. Convert 45 minutes to hours (0.75 hours). Then, 8 km ÷ 0.75 hr = 10.67 km/hr. However, the average speed is calculated as 8 km ÷ 1.2 hr = 6.67 km/hr.

Which equations correctly relate distance, rate, and time? Choose more than one answer.

• dr = t

• r = d/t

• d/r = t

• d = rt

• t + r = d

Answer explanation

The correct equations relating distance (d), rate (r), and time (t) are r = d/t, d/r = t, and d = rt. These formulas express how distance is calculated based on rate and time, and vice versa.