Speed, Time and Distance
- A thief is spotted by a policeman from a distance of 200 m. When the policeman starts chasing, the thief also starts running. If the speed of the thief be 16 km/h and that of the policeman be 20 km/h, how far the thief will have run before he is overtaken?
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Relative speed of policeman = ( 20 - 16 ) x 5/18 = 10/9 m/s
To catch the thief, the policeman in has to gain 200 m = 200 x 9/10 = 180 sCorrect Option: A
Relative speed of policeman = ( 20 - 16 ) x 5/18 = 10/9 m/s
To catch the thief, the policeman in has to gain 200 m = 200 x 9/10 = 180 s
Actual distance covered by policeman in 180 s = 180 x 50/9 = 100 m
∴ Distance covered by the thief = 1000 - 200 = 800m
- A person sets out to cycle from A to B and at the same time another person starts from B to A. After passing each other, they complete their journeys in 16 h and 25 h, respectively. Find the ratio of speeds of the 1st man to that of the 2 nd man.
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Given, x = 16 and Y = 25
According to the formula,
1st man's speed : 2nd man's speed = √ y : √ xCorrect Option: A
Given, x = 16 and Y = 25
According to the formula,
1st man's speed : 2nd man's speed = √ y : √ x = √ 25 : √ 16 = 5 : 4
- A certain distance is covered at a certain speed. If half of this distance is covered in 4 times of the time, then find the ratio of the two speeds.?
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Let L km is covered in T h.
Then, first speed = L/T km/h
Again, L/2 km is covered in 4T h.
∴ New speed = (L/2 x 1/4T ) = (L/8T) km/ hCorrect Option: D
Let L km is covered in T h.
Then, first speed = L/T km/h
Again, L/2 km is covered in 4T h.
∴ New speed = (L/2 x 1/4T ) = (L/8T) km/ h
Ratio of speed = L/T : L/8T = 1 : 1/8 = 8 : 1
- A man covers half of his journey at 6 km/h and the remaining half at 3 km/h. Find his average speed.
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Given, A = 6 km/h, B = 3 km/ h
According to the formula, Average speed = 2AB/(A + B)Correct Option: B
Given, A = 6 km/h, B = 3 km/ h
According to the formula, Average speed = 2AB/(A + B)
∴ Required average speed = 2 x 6 x 3/(6 + 3)
= 36/9 = 4 km/h
- A is twice as fast as B and B is thrice as fast as C. The journey covered by C in 56 min will be covered by A in ?
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Let time taken by A = Y
Let speed of C = x
Then, speed of B = 3x
∴ speed of A = 6x
Now, ratio of speeds of A and C = Ratio of time taken by C and A
6x : x = 56 : yCorrect Option: D
Let time taken by A = Y
Let speed of C = x
Then, speed of B = 3x
∴ speed of A = 6x
Now, ratio of speeds of A and C = Ratio of time taken by C and A
6x : x = 56 : y
⇒ 6x/x = 56/y
∴ y = 56/6 = 92/6
= 91/3 min