## Speed, Time and Distance

#### Speed, Time and Distance

1. In a race of one kilometre, A gives B a start of 100 metres and still wins by 20 seconds. But if A gives B a start of 25 seconds, B wins by 50 metres. The time taken by A to run one kilometre is
1. 17 seconds
2.  500 seconds 29
3.  1200 seconds 29
4.  700 seconds 29

1. Let A take x seconds in covering 1000m and b takes y seconds
According to the question,

 x + 20 = 900 y 1000

 ⇒  x + 20 = 9y ...(i) 10

 and, 950 x + 25 = y     ...(ii) 1000

From equation (i),
 10x + 200 = y 9 9

 ⇒ 10x + 200 = 950x + 25 9 9 1000

 ⇒ 10x + 200 = 19x + 25 9 9 20

 ⇒ 10x − 19x = 25 − 200 9 20 9

 = 200x − 171x = 225 − 200 180 9

 ⇒ 29x = 25 180 9

 ⇒  x = 25 × 180 = 500 seconds. 9 29 29

##### Correct Option: B

Let A take x seconds in covering 1000m and b takes y seconds
According to the question,

 x + 20 = 900 y 1000

 ⇒  x + 20 = 9y ...(i) 10

 and, 950 x + 25 = y     ...(ii) 1000

From equation (i),
 10x + 200 = y 9 9

 ⇒ 10x + 200 = 950x + 25 9 9 1000

 ⇒ 10x + 200 = 19x + 25 9 9 20

 ⇒ 10x − 19x = 25 − 200 9 20 9

 = 200x − 171x = 225 − 200 180 9

 ⇒ 29x = 25 180 9

 ⇒  x = 25 × 180 = 500 seconds. 9 29 29

1. A runs twice as fast as B and B runs thrice as fast as C. The distance covered by C in 72 minutes, will be covered by A in :
1. 18 minutes
2. 24 minutes
3. 16 minutes
4. 12 minutes

1. Ratio of the speed of A, B and
C = 6 : 3 : 1
⇒  Ratio of the time taken

 = 1 : 1 : 1 = 1 : 2 : 6 6 3

 ∴ Time taken by A = 72 = 12 minutes 6

##### Correct Option: D

Ratio of the speed of A, B and
C = 6 : 3 : 1
⇒  Ratio of the time taken

 = 1 : 1 : 1 = 1 : 2 : 6 6 3

 ∴ Time taken by A = 72 = 12 minutes 6

1. In a one-kilometre race A, B and C are the three participants. A can give B a start of 50 m. and C a start of 69 m. The start, which B can allow C is
1. 17 m.
2. 20 m.
3. 19 m.
4. 18 m.

1. Let the time taken to complete the race by A,B, and C be x minutes.

 ∴  Speed of A = 100 , x

 B = 1000 − 50 = 950 x x

 C = 1000 − 69 = 931 x x

Now, time taken to complete the race by
 B = 1000 = 1000 × x 950/x 950

 and distance travelled by C in 1000x min 950

 = 1000x × 931 = 980 km. 950 x

∴  B can allow C
= 1000 – 980 = 20 m

##### Correct Option: B

Let the time taken to complete the race by A,B, and C be x minutes.

 ∴  Speed of A = 100 , x

 B = 1000 − 50 = 950 x x

 C = 1000 − 69 = 931 x x

Now, time taken to complete the race by
 B = 1000 = 1000 × x 950/x 950

 and distance travelled by C in 1000x min 950

 = 1000x × 931 = 980 km. 950 x

∴  B can allow C
= 1000 – 980 = 20 m

1. A train 110 metre long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
1. 5 seconds
2. 6 seconds
3. 7 seconds
4. 10 seconds

1. Relative speed of train
= (60 + 6) kmph.

 = 66 × 5 m/sec. 18

 = 55 m/sec. 3

Length of train = 110 metre
 ∴   Required time = 110 seconds 55/3

 = 110 × 3 seconds 55

= 6 seconds

##### Correct Option: B

Relative speed of train
= (60 + 6) kmph.

 = 66 × 5 m/sec. 18

 = 55 m/sec. 3

Length of train = 110 metre
 ∴   Required time = 110 seconds 55/3

 = 110 × 3 seconds 55

= 6 seconds

1. The time for a train of length 110 metre running at the speed of 72 km/hr to cross a bridge of length 132 metre is
1. 9.8 seconds
2. 12.1 seconds
3. 12.42 seconds
4. 14.3 seconds

1. Speed of train = 72 kmph.

 = 72 × 5 m./sec. 18

= 20 m./sec.
 Required time = Length of train and bridge Speed of train

 = 110 + 132 seconds 20

 = 242 seconds 20

= 12.1 seconds

##### Correct Option: B

Speed of train = 72 kmph.

 = 72 × 5 m./sec. 18

= 20 m./sec.
 Required time = Length of train and bridge Speed of train

 = 110 + 132 seconds 20

 = 242 seconds 20

= 12.1 seconds