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

Emma intends to row down a river and back. The one-way distance is 7 miles. The current flows at 2 miles per hour, while Emma rows at a constant speed of 5 miles per hour in the still water. How long does it take for Emma to row downstream and then return upstream?

  1. 2 hours 20 minutes

  2. 3 hours 15 minutes

  3. 3 hours 20 minutes

  4. 4 hours 10 minutes

  5. 4 hours 20 minutes
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Downstream speed = 5+2=7 mph. Time = 7/7 = 1 hour. Upstream speed = 5-2=3 mph. Time = 7/3 = 2 hours 20 minutes. Total time = 3 hours 20 minutes.

Multiple choice

Marc travels from his home in San Francisco to his office in Las Vegas, covering a total distance of 430 miles. He drives the first 240 miles at a constant speed of 60 miles per hour. For the remaining distance, due to road construction, he drives at a reduced speed of 38 miles per hour. Along the way, he also takes a 30-minute coffee break. What is his approximate average speed for the entire journey, excluding the stoppage time?

  1. 44 miles per hour

  2. 48 miles per hour

  3. 52 miles per hour

  4. 54 miles per hour

  5. 56 miles per hour
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Distance 1 = 240 miles at 60 mph. Time 1 = 240/60 = 4 hours. Distance 2 = 430 - 240 = 190 miles at 38 mph. Time 2 = 190/38 = 5 hours. Total distance = 430 miles. Total time = 4 + 5 = 9 hours. Average speed = 430 / 9 = 47.77 mph, which is approximately 48 mph.

Multiple choice

Stefanie embarks on a road trip from Dallas to Austin, Texas, covering 180 miles. She covers the first 70 miles in 2 hours without any stops. After taking a 1-hour lunch break, she resumes her journey and drives the remaining 110 miles at an average speed of 55 miles per hour. What is her average speed for the entire trip, including the lunch break?

  1. 34 miles per hour

  2. 36 miles per hour

  3. 40 miles per hour

  4. 42 miles per hour

  5. 48 miles per hour
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total distance is 180 miles. Total time is 2 hours (first part) + 1 hour (break) + (110 miles / 55 mph) = 2 + 1 + 2 = 5 hours. Average speed = Total distance / Total time = 180 / 5 = 36 mph.

Multiple choice

A cyclist leaves New York City at 8:00 AM and travels at a constant speed of 15 miles per hour towards Philadelphia. A car leaves New York City at 9:00 AM and travels at a constant speed of 60 miles per hour towards Philadelphia on the same route. At what time will the car overtake the cyclist?

  1. 9:15 AM

  2. 9:20 AM

  3. 9:45 AM

  4. 10:00 AM

  5. 10:15 AM
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The cyclist has a 1-hour head start, covering 15 miles. The relative speed of the car to the cyclist is 60 - 15 = 45 mph. To cover the 15-mile gap, the car needs 15/45 hours, which is 1/3 hour or 20 minutes; thus, it overtakes at 9:20 AM.

Multiple choice

A marathon runner maintains an average speed of 10 miles per hour for the first 15 miles of a marathon and covers the remaining 11.2 miles at an average speed of 5 miles per hour. How much time does the runner take to complete the marathon?

  1. 3 hours

  2. 3.5 hours

  3. 3.74 hours

  4. 4.24 hours

  5. 4.5 hours
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Time 1 = 15 miles / 10 mph = 1.5 hours. Time 2 = 11.2 miles / 5 mph = 2.24 hours. Total time = 1.5 + 2.24 = 3.74 hours.

Multiple choice

Alex notices a yacht that has already sailed 60 nautical miles out of a 100-nautical-mile course. Initially, the yacht is cruising at a speed of 8 knots in calm waters. Suddenly, it catches a favorable current of 2 knots, pushing it in the same direction. If t represents the time taken in hours to cover the remaining distance, which equation below best describes this scenario? [1 knot = 1 nautical mile per hour]

  1. 60 = 40 + 8t

  2. 100 = 60 + 10t

  3. 100 = 40 + 9.2t

  4. 160 = 11.5t + 40
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Remaining distance = 100 - 60 = 40 nautical miles. Speed = 8 + 2 = 10 knots. Time t = distance / speed, so 40 = 10t. The total distance 100 is equal to the distance already covered (60) plus the distance covered in time t (10t). Thus, 100 = 60 + 10t.

Multiple choice

On a family road trip to his grandparents' house, Alex drives a total distance of 180 miles. He travels at an average speed of 50 miles per hour for the first x hours and then completes the trip by switching to a speed of 40 miles per hour to enjoy the scenery along the route for the remaining y hours. If x = 2, what is the value of y?

  1. 2

  2. 3

  3. 4

  4. 5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Alex drives 50 mph for 2 hours, covering 100 miles. The remaining distance is 180 - 100 = 80 miles. At 40 mph, the time y taken is 80 / 40 = 2 hours.

Multiple choice

The uniform speed Of a motorboat in upstream is 12 km per hour and its downstream speed is 18 km per hour. The motorboat goes from point P to point Q in upstream and returns the same distance in downstream. What is its average speed of the entire journey? (the speed Of the motorboat and stream was uniform during the entire journey)

  1. 15 km hour

  2. 14.8 km per hour

  3. 14.2 km per hour

  4. 14.4 km per hour
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Average speed for a round trip is 2xy / (x+y), where x and y are the upstream and downstream speeds. Average speed = 2 * 12 * 18 / (12 + 18) = 432 / 30 = 14.4 km/hr.

Multiple choice

Carlos and Maria rode for two parts of the trip, and the total distance they rode was less than 150 miles. Carlos rode at an average speed of 20 mph for the first part of the trip, and Maria rode at an average speed of 25 mph for the second part. Which inequality represents this situation, where c is the number of hours Carlos rode and m is the number of hours Maria rode?

  1. 20c + 25m < 150

  2. 25c + 20m < 150

  3. 20c + 25m ≤ 150

  4. 25c + 20m ≤ 150
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Distance is speed multiplied by time. Carlos's distance is 20c and Maria's distance is 25m. The total distance 20c + 25m is stated to be less than 150 miles, which is represented by the inequality 20c + 25m < 150.

Multiple choice

Emma is a professional photographer who travels frequently for her assignments. On one of her trips, she needs to travel from City P to City Q, which are 420 miles apart. She starts her journey from City P at 8:00 AM and drives at a constant speed of 60 miles per hour. After covering half the distance, she takes a break for lunch, which lasts for 45 minutes. After the break, she continues her journey at a reduced speed of 50 miles per hour due to road conditions. What time does Emma arrive in City Q?

  1. 2:16 PM

  2. 2:37 PM

  3. 3:27 PM

  4. 4:27 PM

  5. 5:15 PM
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total distance 420 miles. First half (210 miles) at 60 mph takes 3.5 hours. Start 8:00 AM + 3.5 hours = 11:30 AM. Lunch 45 mins = 12:15 PM. Remaining 210 miles at 50 mph takes 4.2 hours (4 hours 12 minutes). 12:15 PM + 4 hours 12 minutes = 4:27 PM.

Multiple choice

Josh is an avid cyclist training for an upcoming marathon. He starts his training by cycling from his home to a nearby town at a speed of 15 miles per hour. On the way back by the same route, he reduces his speed to 10 miles per hour due to an uphill climb. The entire round trip takes him 2.5 hours. What is the distance between Josh's home and the nearby town?

  1. 10 miles

  2. 12 miles

  3. 15 miles

  4. 20 miles

  5. 25 miles
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let d be the distance. The total time is d/15 + d/10 = 2.5. Multiplying by 30 gives 2d + 3d = 75, so 5d = 75, which means d = 15 miles.