Quantitative Aptitude Notes Part 12( Speed, Time and distance)

Speed, Time and distance

Basic Formula of speed and distance

  • Distance = Speed x Time
  • Speed = Distance / Time
  • Time = Distance / Speed

1 km. /hour =  m. /sec

1 m. /sec =  km. /hour

Example:
Arjun goes to his college from his house at a speed of 3 Km / hr and return at speed of 2 km / hr. If he takes 5 hours in going and coming, the distance between his house and college is-
Answer:
Average speed = ( ) km / hr = km / hr.
Distance between his house and college he travelled : ( x 5 ) km = 12 km .

Example:
How many minutes does Seema take to cover a distance of 600 m, if she runs at speed of 40 km / hr ?
Answer:
Seema speed = 40 km / hr,.
(40 x ) = m / sec     (after converting it into m / sec)
So, Seema Time taken to cover 600 m = (600 x ) sec = 54 sec.
So Seema Time taken to cover distance 54 sec.

Example:
Harish on tour travels first 160 km at 64 km /hr and the next 160 km at 80 km /hr . The average speed of for the first 320 km of the tour  is :
Answer:
Total time taken  by Harish is : = ( + ) hrs = hrs .
So that Average speed = (320 x ) km / hr = 71.11 km / hr

Example:
A car completes a journey in 12 hours , the first half hours complete at 23 km / hr and the second half at 25 km / hr . Find the distance?
Answer:
let the distance be x km .
Time taken by the car to complete the  km at a speed of 23 km / hr
the car has time taken to complete the km at a speed of 25 km / hr
So , total time taken to complete the whole journey is ,
= 23 +    25 = 10 hrs
x =
x =287.5
Shortcut tricks: Distance =  Here S1 = speed during first half and S2 = Speed of second half of journey
Distance = = 287.5 km .

Example:
With a uniform speed a bike covers the distance in 10 hours. When speed of bike is increased by 4 km / hr, the same distance could have been covered in 8 hours. What is the distance covered by bike?
Answer:
let the distance be x km .Then ,
–  = 4
x = 160 km .

Example:
A Truck covers a certain distance in 7 hours at the speed of 73 Kms/hr. What is average speed of bus? Which travels a distance of 55 Kms. less than the Truck in the same time?
Answer:
Step 1 : The distance covered by the Truck = ( 73 x 7 ) = 511
Step 2 : The distance cover bus = 511 – 55 = 456 Km.

So, average speed of the bus =  = 91.2 Km/hr.

 

Example: 
The ratio between two super fast trains is 6 : 8. if the second train runs 600 Kms in 6 hours, then what would be the speed of the first train ?
Answer:
Step 1: Let the speed of two trains be 6x and 8x Km /hr.
Then, then we find the value of x,
8x = = 100
x = = 12.5.
Here, value of x is 12.5 we put in first train.
Step 2: Speed of first would be = (6 x 12.5) Km / hr =75 Km / hr.
So the Speed of First train is 75 Km / hr.

 

Example:
A boy without any stoppage  running on a road at an average speed of 80 km /hr , and with stoppage he covers the same distance at an average speed of 60 km / hr . How many minutes per hour does boy stop?
Answer:
Let the total distance cover by boy on road is  x km .
Time take to complete at a speed of 80 km / hours = x / 80 hours.
Time take to complete at a speed of 80 km / hours = x / 60 hours.
So he stop to rest ( – ) hours =  = .
So he rest per hour = / = ( ) x ( ) = hours = 15 minutes.

Shortcut Tricks:
Time of rest per hour = ( Difference of speed/ Speed without stoppage )
= = 15 minutes

Example:
A man walking at the rate of 4kmph to cover certain distance in 2hr 45 min. Running at a speed of 16.5 kmph the man will cover the same distance in what time?
Answer:
By the formula of  Distance = speed x Time
So, Time given = 2hr 45min = 2x 60min+ 45min= 165min

= hr
Distance = 4 x = 11 km
So, Time required to cover distance in speed of 16.5kmph
Time = D / S = 11 / 16.5 = 40min.

 


Example:
A train traveling at 90 kmph overtakes a bike traveling at 54 kmph in 30 seconds. What is the length of the train in meters?
Answer:
The distance travailed by the train overtaking the bike is the same as the length of the train.
Both the object move in same direction.
So, (90 – 54) = 36kmph
convert kmph to m/sec = 36 x = 10 m / sec.
Time taken in 40 sec.
distance travailed = 10 x 30 = 300 meters.

 

Click here to join our Facebook Group for SSC Preparation, latest News and Discussion

Leave a Reply