Time and Distance Problems and Solutions

• 1. The ratio between the speeds of two trains is 7: 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is ?

  1. 83.5 km/hr
  2. 84.5 km/hr
  3. 86.5 km/hr
  4. 87.5 km/hr

  Answer :

  Option D

  Explanation:

  Let the speeds of two trains be 7X and 8X km/hr.
  
  \begin{aligned}
  8X = \frac{400}{4} \\
  => X = 12.5 Km/hr
  
  \end{aligned}
  So speed of first train is 12.5*7 = 87.5 km/hr

• 2. A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes ?

  1. 50 meter
  2. 100 meter
  3. 110 meter
  4. None of above

  Answer :

  Option B

  Explanation:

  Relative speed of the thief and policeman = (11 – 10) km/hr = 1 km/hr
  
  Distance covered in 6 minutes =
  \begin{aligned}
  \frac{1}{60}*6 = \frac{1}{10} \\
  = 100 meters
  \end{aligned}
  
  So distance between them after 6 minutes = 200 - 100
  = 100 meters

• 3. An athlete runs 200 meters in 24 seconds. His speed is ?

  1. 10 km/hr
  2. 17 k/hr
  3. 27 km/hr
  4. 30 km/hr

  Answer :

  Option D

  Explanation:

  \begin{aligned}
  Speed = \frac{Distance}{Time} \\
  = \frac{200}{24}m/sec = \frac{25}{3} m/sec \\
  \frac{25}{3}*\frac{18}{5} km/hr = 30 km/hr
  \end{aligned}

• 4. A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. Find the average speed for first 320 km of tour.

  1. 70.11 km/hr
  2. 71.11 km/hr
  3. 72.11 km/hr
  4. 73.11 km/hr

  Answer :

  Option B

  Explanation:

  We know Time = Distance/speed
  
  So total time taken =
  \begin{aligned}
  \left(\frac{160}{64}+\frac{160}{80}\right) \\
  = \frac{9}{2} hours \\
  \text{ Time taken for 320 Km = } \\
  320*\frac{2}{9} = 71.11 km/hr
  \end{aligned}

• 5. A Man travelled a distance of 61 km in 9 hours. He travelled partly on foot at 4 km/hr and partly on bicycle at 9 km/hr. What is the distance travelled on foot?

  1. 16 km
  2. 14 km
  3. 12 km
  4. 10 km

  Answer :

  Option A

  Explanation:

  Let the time in which he travelled on foot = x hour
  Time for travelling on bicycle = (9 - x) hr
  
  Distance = Speed * Time, and Total distance = 61 km
  So,
  4x + 9(9-x) = 61
  => 5x = 20
  => x = 4
  
  So distance traveled on foot = 4(4) = 16 km

• 6. Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?

  1. 9 km/hour
  2. 10 km/hour
  3. 11 km/hour
  4. 12 km/hour

  Answer :

  Option D

  Explanation:

  We need to calculate the distance, then we can calculate the time and finally our answer.
  Lets solve this,
  
  Let the distance travelled by x km
  Time = Distance/Speed
  
  \begin{aligned}
  \frac{x}{10} - \frac{x}{15} = 2 \\
  \text{[because, 2 pm - 12 noon = 2 hours]} \\
  
  3x - 2x = 60 \\
  x = 60.
  
  Time = \frac{Distance}{Speed} \\
  Time @ 10km/hr = \frac{60}{10} = 6 hours
  
  \end{aligned}
  So 2 P.M. - 6 = 8 A.M
  Robert starts at 8 A.M.
  
  He have to reach at 1 P.M. i.e, in 5 hours
  
  So, Speed = 60/5 = 12 km/hr
  

• 7. A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.

  1. 200 Km
  2. 222 Km
  3. 224 Km
  4. 248 Km

  Answer :

  Option C

  Explanation:

  Let time taken to travel the first half = x hr
  Then time taken to travel the second half = (10 - x) hr
  
  Distance covered in the the first half = 21x [because, distance = time*speed]
  Distance covered in the the second half = 24(10 - x)
  
  Distance covered in the the first half = Distance covered in the the second half
  So,
  21x = 24(10 - x)
  => 45x = 240
  => x = 16/3
  
  Total Distance = 2*21(16/3) = 224 Km [multiplied by 2 as 21x was distance of half way]