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 rail engine is moving at a uniform speed of 30 km per hour towards a place A. When the engine is still 20 km away from A, an insect starts at A and shuttles between A and engine at a uniform speed of 42 km per hour. The total distance travelled by the insect, by the time engine reaches A is, in km.

  1. 28

  2. 30

  3. 20

  4. 42
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Time for engine to reach A = 20 km / 30 km/h = 2/3 hours. Insect speed = 42 km/h. Distance = Speed * Time = 42 * (2/3) = 28 km.

Multiple choice

On a race, Anjali ran $\dfrac {3}{4}$ of the time with a good-luck cabbage, and $\dfrac {1}{4}$ of the time without it. With the cabbage, her running speed was $6$ miles per hour, and her running speed without the cabbage was $12$ miles per hour. The distance that Anjali ran with the cabbage was what fraction of the total distance that she ran?
  1. $0.6$
  2. $0.8$
  3. $0.9$
  4. $0.4$
  5. $0.5$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let T be the total time. Distance with cabbage = (3/4)T * 6 = 4.5T. Distance without cabbage = (1/4)T * 12 = 3T. Total distance = 4.5T + 3T = 7.5T. Fraction = 4.5T / 7.5T = 4.5 / 7.5 = 0.6.

Multiple choice

At $10:00$, Angela starts from her home and runs at a constant pace to Kathleens house, which is exactly $2$ miles away. Immediately, she and Kathleen turn around and walk back to Angelas house exactly $4$ miles an hour slower than Angela ran. When they arrive at Angelas house, the time is $10:45$. At what speed did Angela run?
  1. $6$ miles per hour
  2. $6.5$ miles per hour
  3. $7$ miles per hour
  4. $7.5$ miles per hour
  5. $8$ miles per hour
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let speed be v. Time to house = 2/v. Return speed = v - 4. Return time = 2/(v-4). Total time = 45 min = 0.75 hours. 2/v + 2/(v-4) = 0.75. 2(v-4 + v) / (v(v-4)) = 0.75. 2(2v-4) = 0.75(v^2 - 4v). 4v - 8 = 0.75v^2 - 3v. 0.75v^2 - 7v + 8 = 0. Multiply by 4/3: v^2 - 9.33v + 10.66 = 0. Roots are 8 and 1.33. Since speed must be > 4, v = 8.

Multiple choice

Two people set off by car on a rally and take the same route which is $25$ miles long. If $A$ drives at an average speed of $50$ miles per hour and $B$ at an average speed of $60$ miles per hour, how much longer in minutes will it take $A$ to cover the course than it takes $B$?
  1. $5$ minutes
  2. $6$ minutes
  3. $8$ minutes
  4. $10$ minutes
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Time for A = 25 miles / 50 mph = 0.5 hours = 30 minutes. Time for B = 25 miles / 60 mph = 25/60 hours = 25 minutes. Difference = 30 - 25 = 5 minutes.

Multiple choice

A train travels $40$% faster than a car. Both start from point A at the same time and reach point B, $140km$ away at the same time. On the way the train takes $25$ minutes for stopping at the stations. What is the speed (in km/hr) of the train?
  1. $67$
  2. $134.4$
  3. $145.9$
  4. $160$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let car speed be v. Train speed is 1.4v. Time for car = 140/v. Time for train = 140/(1.4v) + 25/60. Since times are equal: 140/v = 100/v + 5/12. 40/v = 5/12, so v = 96 km/hr. Train speed = 1.4 * 96 = 134.4 km/hr.

Multiple choice

A man travels the first part of his journey at $20$ km/hr and the next at $70$ km/h, covering the entire journey at an average speed of $50 $km/h. What is the ratio of the distance that the covered at $20$ km/h to that he covered at $70 $km/h?
  1. $4:21$
  2. $3:22$
  3. $1:4$
  4. $3:5$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let distances be d1 and d2. Average speed = Total Distance / Total Time = (d1+d2) / (d1/20 + d2/70) = 50. (d1+d2) / ((7d1+2d2)/140) = 50. 140(d1+d2) = 50(7d1+2d2). 14d1 + 14d2 = 35d1 + 10d2. 4d2 = 21d1. d1/d2 = 4/21.