Quantitative Aptitude

Time, Speed and Distance

2,165 Questions
All Core formulas and unit conversion 441 Boats and streams effective speed 396 Relative speed, meetings, and overtaking 375 Average speed 362 Early and late arrival 321 Proportional relationships 202 Stoppage time per hour 35 Train and stationary or moving object crossing 17 Races and dead heats 16

Time, Speed and Distance Questions

Multiple choice

A train travels from City A to City B at a speed of 60 mph. On the return journey, the train travels at a speed of 75 mph. If the total time taken for the round trip is 5 hours, what is the distance between City A and City B?

  1. 187.5 miles

  2. 200 miles

  3. 212.5 miles

  4. 225 miles
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the distance between City A and City B be x miles. The time taken for the journey from City A to City B is x / 60 hours, and the time taken for the journey from City B to City A is x / 75 hours. The total time taken for the round trip is the sum of these two times, which is (x / 60) + (x / 75) = 5 hours. Solving for x, we get x = 200 miles.

Multiple choice

A train leaves Chicago at 10:00 AM and travels at a speed of 60 miles per hour. Another train leaves St. Louis at 11:00 AM and travels towards Chicago at a speed of 70 miles per hour. If the distance between Chicago and St. Louis is 300 miles, at what time will the two trains meet?

  1. 1:00 PM

  2. 1:30 PM

  3. 2:00 PM

  4. 2:30 PM
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The first train travels for 1 hour before the second train leaves. In that time, it travels 60 miles. So, when the second train leaves, there are 240 miles left to travel. The two trains are traveling at a combined speed of 130 miles per hour. So, it will take them 2 hours to travel the remaining distance. Therefore, they will meet at 2:00 PM.

Multiple choice

A train leaves a station at (10:00) AM and travels at a speed of (60) miles per hour. Another train leaves the same station at (11:00) AM and travels in the same direction at a speed of (70) miles per hour. At what time will the second train be (100) miles ahead of the first train?

  1. \(12:00\) PM
  2. \(1:00\) PM
  3. \(2:00\) PM
  4. \(3:00\) PM
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To find the time at which the second train is (100) miles ahead of the first train, we need to calculate the relative speed between them. The relative speed is the difference between the speeds of the two trains: (70 - 60 = 10) miles per hour. Then, we need to find the distance between the two trains at (11:00) AM. The first train travels for (1) hour at a speed of (60) miles per hour, so it travels (60) miles. Therefore, the distance between the two trains at (11:00) AM is (60) miles. Now, we can divide the distance between the two trains by the relative speed to find the time it takes for the second train to be (100) miles ahead of the first train: (100 / 10 = 10) hours. Since the second train leaves at (11:00) AM, it will be (100) miles ahead of the first train at (11:00) AM + (10) hours = (1:00) PM.

Multiple choice

A train travels a distance of 300 kilometers in 5 hours. What is the average speed of the train?

  1. 50 km/h

  2. 60 km/h

  3. 70 km/h

  4. 80 km/h
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The average speed of the train is (300 \div 5 = 60) km/h.

Multiple choice

A car is moving at a speed of 60 km/h. What is the distance travelled by the car in 1 hour?

  1. 60 km

  2. 120 km

  3. 180 km

  4. 240 km
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The distance travelled by the car in 1 hour is given by the equation $s = vt$. Substituting the values, we get $s = 60 * 1 = 60 km$.

Multiple choice

A train is moving at a speed of 90 km/h. What is the time taken by the train to travel a distance of 180 km?

  1. 1 hour

  2. 2 hours

  3. 3 hours

  4. 4 hours
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The time taken by the train to travel a distance of 180 km is given by the equation $t = s/v$. Substituting the values, we get $t = 180/90 = 2 hours$.

Multiple choice

A boat is moving at a speed of 10 m/s. What is the distance travelled by the boat in 5 minutes?

  1. 300 m

  2. 600 m

  3. 900 m

  4. 1200 m
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The distance travelled by the boat in 5 minutes is given by the equation $s = vt$. Substituting the values, we get $s = 10 * 5 * 60 = 300 m$.

Multiple choice

A cyclist is moving at a speed of 15 km/h. What is the time taken by the cyclist to travel a distance of 10 km?

  1. 20 minutes

  2. 30 minutes

  3. 40 minutes

  4. 50 minutes
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The time taken by the cyclist to travel a distance of 10 km is given by the equation $t = s/v$. Substituting the values, we get $t = 10/15 = 40/60 = 40 minutes$.

Multiple choice

A train travels 240 miles in 4 hours. If the train increases its speed by 20%, how long will it take to travel the same distance?

  1. 3 hours 12 minutes

  2. 3 hours 24 minutes

  3. 3 hours 36 minutes

  4. 3 hours 48 minutes
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

New speed = 120 * 120% = 144 mph Time to travel 240 miles = 240 / 144 = 3.33 hours = 3 hours 20 minutes

Multiple choice

A train travels 360 miles in 6 hours. If the train decreases its speed by 20%, how long will it take to travel the same distance?

  1. 7 hours 12 minutes

  2. 7 hours 24 minutes

  3. 7 hours 36 minutes

  4. 7 hours 48 minutes
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

New speed = 360 * 80% = 288 mph Time to travel 360 miles = 360 / 288 = 6.25 hours = 6 hours 15 minutes

Multiple choice

A boatman rows to a place 45 km distant and back in 20 hours. He finds that he can row 12 km with the stream in the same time as 4 km against the stream. Find the speed of the stream.

  1. 3 km/hr

  2. 2.5 km/hr

  3. 4 km/hr

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let boat speed be u and stream speed be v. 12/(u+v) = 4/(u-v) => 12u - 12v = 4u + 4v => 8u = 16v => u = 2v. Total time = 45/(u+v) + 45/(u-v) = 20. 45/(3v) + 45/v = 20 => 15/v + 45/v = 20 => 60/v = 20 => v = 3 km/hr.

Multiple choice

A plane left 30 minutes later than its scheduled time. If it had to increase its usual speed by 250 km/hr in order to reach the destination 1500 km away on time, then which of the following options is true?

  1. Usual speed of the plane was 850 km/hr.

  2. Increased speed of the plane was 1000 km/hr.

  3. The plane will cover 750 km in 1.5 hours on travelling with usual speed.

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let v be usual speed. 1500/v - 1500/(v+250) = 0.5. 3000(v+250) - 3000v = v(v+250). 750000 = v^2 + 250v. v^2 + 250v - 750000 = 0. (v+1000)(v-750) = 0. v = 750. Increased speed = 1000.