Time and Distance Problems and Solutions

• 8. A man in a train notices that he can count 41 telephone posts in one minute. If they are known to be 50 metres apart, then at what speed is the train travelling?

  1. 60 km/hr
  2. 100 km/hr
  3. 110 km/hr
  4. 120 km/hr

  Answer :

  Option D

  Explanation:

  Number of gaps between 41 poles = 40
  So total distance between 41 poles = 40*50
  = 2000 meter = 2 km
  In 1 minute train is moving 2 km/minute.
  Speed in hour = 2*60 = 120 km/hour

• 9. How many minutes does Aditya take to cover a distance of 400 m, if he runs at a speed of 20 km/hr

  1. \begin{aligned} 1\frac{1}{5} min\end{aligned}
  2. \begin{aligned} 2\frac{1}{5} min\end{aligned}
  3. \begin{aligned} 3\frac{1}{5} min\end{aligned}
  4. \begin{aligned} 4\frac{1}{5} min\end{aligned}

  Answer :

  Option A

  Explanation:

  We know that,
  \begin{aligned}
  Time = \frac{Distance}{Speed} \\
  Speed = 20\text{ km/hr} = 20*\frac{5}{18}{ m/sec} \\
  = \frac{50}{9}{ m/sec} \\
  
  \text{ Time =} \left(400*\frac{9}{50}\right) \\
  = 72 {sec} = 1\frac{1}{5}{ min}
  \end{aligned}
  
  

• 10. A person travels from P to Q at a speed of 40 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips ?

  1. 44 km/hour
  2. 46 km/hour
  3. 48 km/hour
  4. 50 km/hour

  Answer :

  Option C

  Explanation:

  Speed while going = 40 km/hr
  Speed while returning = 150% of 40 = 60 km/hr
  
  Average speed =
  \begin{aligned}
  \frac{2xy}{x+y} \\
  = \frac{2*40*60}{40+60} = \frac{4800}{100} \\
  = 48 Km/hr
  \end{aligned}
  

• 11. A person travels equal distances with speed of 3 km/hr, 4 km/hr and 5 km/hr and takes a total of 47 minutes. Find the total distane

  1. 3 km
  2. 4 km
  3. 6 km
  4. 9 km

  Answer :

  Option A

  Explanation:

  Let the distance be 3x km,
  then,
  \begin{aligned}
  \frac{x}{3} +\frac{x}{4} +\frac{x}{5} = \frac{47}{60} \\
  \frac{47x}{60} =\frac{47}{60} \\
  x = 1
  \end{aligned}
  So total distance = 3*1 = 3 Km

• 12. A car moves at 80 km/hr. What is the speed of the car in meters per second ?

  1. \begin{aligned} 20\frac{2}{9} m\sec \end{aligned}
  2. \begin{aligned} 22\frac{2}{9} m\sec \end{aligned}
  3. \begin{aligned} 24\frac{2}{9} m\sec \end{aligned}
  4. \begin{aligned} 26\frac{2}{9} m\sec \end{aligned}

  Answer :

  Option B

  Explanation:

  \begin{aligned}
  Speed = \left(80*\frac{5}{18}\right) m/sec \\
  = \frac{200}{9} m/sec \\
  = 22\frac{2}{9} m\sec
  \end{aligned}

• 13. In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. What is the duration of the flight ?

  1. 3 hours
  2. 2.4 hours
  3. 1.4 hours
  4. 1 hour

  Answer :

  Option D

  Explanation:

  Let the duration of the flight be x hours.
  Then
  \begin{aligned}
  \frac{600}{x}-\frac{600}{x + \frac{1}{2}} = 200 \\
  \frac{600}{x}-\frac{1200}{2x+1} = 200 \\
  x(2x+1) = 3 \\
  2x^2 + x - 3 = 0 \\
  => (2x+3)(x-1)=0
  
  \end{aligned}
  Neglecting the negative value for x we get x = 1

• 14. A cyclist covers a distance of 750 meter in 2 minutes 30 seconds. What is the speed in km/hr of cyclist

  1. 16 km/hr
  2. 17 km/hr
  3. 18 km/hr
  4. 19 km/hr

  Answer :

  Option C

  Explanation:

  \begin{aligned}
  Speed = \frac{Distance}{Time} \\
  Distance = 750 meter \\
  Time = \text{2 min 30 sec} = 150 sec \\
  Speed = \frac{750}{150} = 5 m/sec \\
  
  => 5*\frac{18}{5} km/hr = 18 km/hr
  \end{aligned}