Quantitative Aptitude

Time, Speed and Distance

2,165 Questions
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Time, Speed and Distance Questions

Multiple choice

John and Sarah are riding their bikes in a clockwise direction around a circular track that is 600 meters in circumference. They maintain a constant speed, with John covering a distance of 1,200 meters every eight minutes and Sarah covering the same distance every ten minutes. If John and Sarah commence their cycling from opposite points on the circular track, how long will it take for John to cycle and catch up with Sarah second time?

  1. 20 minutes

  2. 30 minutes

  3. 35 minutes

  4. 45 minutes

  5. 48 minutes
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

John speed = 1200/8 = 150 m/min. Sarah speed = 1200/10 = 120 m/min. Relative speed = 150 - 120 = 30 m/min. They start at opposite points (300m apart). To catch up the first time, John must cover the 300m gap. Time = 300 / 30 = 10 min. To catch up the second time, he must cover another 600m (the full track). Time = 600 / 30 = 20 min. Total time = 10 + 20 = 30 min.

Multiple choice

John departed from his residence at 8:30 am to attend a business meeting scheduled for 9:45 am. Driving for 40 minutes at an average speed of 25 miles per hour, he recognized that he was behind schedule. To compensate for the delay, he boosted his speed by 30% and managed to arrive precisely on time. What is the distance between John's house and the place of business meeting?

  1. 25.625 miles

  2. 30.5 miles

  3. 32.625 miles

  4. 35.625 miles

  5. 45.625 miles
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial speed = 25 mph. Time = 40 mins = 2/3 hours. Distance = 25 * 2/3 = 50/3 miles. Time remaining = 9:45 - 8:30 = 75 mins. Time spent = 40 mins. Time left = 35 mins. New speed = 25 * 1.3 = 32.5 mph. Distance covered in 35 mins = 32.5 * (35/60) = 32.5 * (7/12) = 18.958 miles. Total distance = 16.66 + 18.958 = 35.625 miles.

Multiple choice

A flight, travelling to a destination 11,200 kms away, was supposed to take off at 6:30 AM. Due to bad weather, the departure of the flight got delayed by three hours. The pilot increased the average speed of the airplane by 100 km/hr from the initially planned average speed, to reduce the overall delay to one hour. Had the pilot increased the average speed by 350 km/hr from the initially planned average speed, when would have the flight reached its destination?

  1. 11:30 PM

  2. 7:50 PM

  3. 5:10 PM

  4. 8:10 PM

  5. 10:36 PM
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

A group of friends decided to go on a road trip. They rented a car for a certain duration and planned to drive at different speeds during their journey. During the first half of the trip, they travelled at a speed of 60 km/h, and in the second half, they increased their speed to 80 km/h. The total duration of their trip was 6 hours. Find the total distance travelled by them.

  1. 320.43 km

  2. 411.43 km

  3. 420 km

  4. 480 km
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let total distance be D. Time = (D/2)/60 + (D/2)/80 = 6. D/120 + D/160 = 6. (4D + 3D) / 480 = 6. 7D = 2880. D = 411.43 km.

Multiple choice

A car after covering ½ of a journey of 100 km develops engine trouble and later travels at ½ of its original speed. As a result, it arrives 2 hours late than its normal time. What is the normal speed of the car is?

  1. 50 kmph

  2. 40 kmph

  3. 30 kmph

  4. 25 kmph
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Normal time = 100/v. First half (50km) at speed v takes 50/v. Second half (50km) at v/2 takes 100/v. Total time = 50/v + 100/v = 150/v. Difference: 150/v - 100/v = 2. 50/v = 2, so v = 25 kmph.

Multiple choice

Alice and her brother Bob decide to ride bicycles from their house to a park, which is 3.90 miles away. At 9:00 A.M., Alice begins riding toward the park, at a speed of 10 miles per hour. At 9:10 A.M., Bob starts and heads toward the park, but at a faster speed of 15 miles per hour. How long does it take for Bob to reach the park after Alice?

  1. 1 minute

  2. 1 minutes and 35 seconds

  3. 2 minutes

  4. 2 minutes and 12 seconds

  5. 5 minutes
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

After noting down the odometer reading, which showed the smallest four-digit square number, Rimzim started driving to school at a constant speed at 9:00 A.M. After one hour, he realized he would be late and doubled his speed. He reached school at 11:00 A.M. In the school parking lot, he noticed that the odometer now showed the smallest four-digit number that reads the same from both sides and is greater than 1200. What was Rimzim's speed at 9:50 A.M.?(round to one decimal place)

  1. 55.5 km/hr

  2. 60.5 km/hr

  3. 65.7 km/hr

  4. 68.6 km/hr
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The smallest 4-digit square is 32^2 = 1024. The smallest 4-digit palindrome > 1200 is 1221. The distance covered is 1221 - 1024 = 197 km. Let v be the initial speed. He drives 1 hour at v and 1 hour at 2v, covering 3v = 197 km. Thus, v = 65.66... km/hr. Since the speed was constant until 10:00 A.M., the speed at 9:50 A.M. is 65.7 km/hr.

Multiple choice

A boy takes 3 hours more when he decreases his speed by 40 miles per hour. If the total distance is 240 miles, what was his actual speed?

  1. 80 miles per hour

  2. 90 miles per hour

  3. 120 miles per hour

  4. 125 miles per hour

  5. 130 miles per hour
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let speed be v. Time taken at speed v is 240/v. Time taken at speed (v-40) is 240/(v-40). The difference is 240/(v-40) - 240/v = 3. Solving this quadratic equation: 240v - 240(v-40) = 3v(v-40) leads to 9600 = 3v^2 - 120v, or v^2 - 40v - 3200 = 0. Factoring gives (v-80)(v+40) = 0, so v = 80.