Basic Formula of speed and distance
- Distance = Speed x Time
- Speed = Distance / Time
- Time = Distance / Speed
Formula:
- B km / hr convert to m / sec = ( B x 5 / 18) m / sec.
- B m / sec convert to km / sec =(B x 18 / 5 ) km / sec.
If the ratio of the speeds of A and B is a : b, then the ratio of the times taken by them to cover the same distance is 1 / a : 1 / b or b : a .
Suppose a man covers a certain distance at x km / hr and an equal distance at y km / hr. Then, average speed during the whole journey is 2 x y / (x + y ) km / hr. which came from the formula 2/(1/x + 1/y)
Example 1 :
A girl goes to his college from her house at a speed of 3 Km / hr and return at speed of 2 km / hr . If she takes 5 hours in going and coming , the distance between her house and colloge is :
Answer :
Average speed = ( 2 x 3 x 2 / 2 + 3 ) km / hr = 12 / 5 km / hr.
Distance between her house and college she travailed : ( 12 / 5 x 5 ) km = 12 km .
Example 2:
How many minutes does Rakesh take to cover a distance of 600 m, if he runs at speed of 40 km / hr ?
Answer :
Rakesh speed = 40 km / hr first we convert it into m / sec .
( 40 x 5 / 18 ) = 100 / 9 m / sec
So , Rakesh Time taken to cover 600 m = (600 x 9 / 100 ) sec = 54 sec.
So Rakesh Time taken to cover distance 54 sec.
Example 3:
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 : = ( 160 / 64 + 160 / 8 ) hrs = 9 / 2 hrs .
So that Average speed = ( 320 x 2 / 9 ) km / hr = 71.11 km / hr .
Example 4:
A Honda car does complete 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 is
Answer :
let the distance be x km .
the car has time taken to complete the x / 2 km at a speed of 23 km / hr .
the car has time taken to complete the x / 2 km at a speed of 25 km / hr .
So , total time taken to complete the whole journey is ,
= x / 2 x 23 + x / 2 x 25 = 10 hrs
x = 2 x 10 x 23 x 25 / ( 23 + 25 )
x =287.5
Shortcut tricks : Distance = 2 x Time x speed 1 x speed 2 / s1 + s2
Here s1 = speed during first half and s2 = Speed of second half of journey
Distance = 2 x 10 x 23 x 25 / ( 23 + 25 ) = 287.5 km .
Example 5:
A bike covers a distance of 450 m in 2 min 30 sec.What is the speed in Km / hr of the bike ?
Answer :
Step 1: Speed = ( 450 / 150 ) m / sec = 3 m / sec.
Step 2: now convert it into km / hr = 3 x 18 / 5 = 10.8 Km / hr.
So the speed of in Km / hr of the bike is 10.8 Km / hr .
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