## Speed, Time and Distance

#### Speed, Time and Distance

1. A train moves with a speed of 30 kmph for 12 minutes and for next 8 minutes at a speed of 45 kmph. Find the average speed of the train:
1. 37.5 kmph
2. 36 kmph
3. 48 kmph
4. 30 kmph

1.  Average speed = Total distance time taken

 = 30 × 12 + 45 × 8 60 60 12 + 8 60 60

= 12 × 3 = 36 kmph

##### Correct Option: B

 Average speed = Total distance time taken

 = 30 × 12 + 45 × 8 60 60 12 + 8 60 60

= 12 × 3 = 36 kmph

1. A person travels 600 km by train at 80km/hr, 800 km by ship at 40 km/hr 500 km by aeroplane at 400 km/hr and 100 km by car at 50km/hr. What is the average speed for the entire distance ?
1.  65 5 km./hr. 123
2. 60 km./hr.
3.  60 5 km./hr. 123
4. 62 km./hr.

1.  Total time = 600 + 800 + 500 + 100 80 40 400 50

 = 246 hours. 8

 Average speed = 600 + 800 + 500 +100 246 8

 = 2000 × 8 246

 = 65 5 km/hr. 123

##### Correct Option: A

 Total time = 600 + 800 + 500 + 100 80 40 400 50

 = 246 hours. 8

 Average speed = 600 + 800 + 500 +100 246 8

 = 2000 × 8 246

 = 65 5 km/hr. 123

1. A boy rides his bicycle 10km at an average speed of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. His average speed for the entire trip is approximately :
1. 10.4 km/hr
2. 10.8 km/hr
3. 11.0 km/hr
4. 12.2 km/hr

1. Total distance = 10 + 12 = 22 km

 Total time = 10 + 12 12 10

 = 244 hours 120

 ∴  Required average speed = Total distance Total time

 = 22 244 120

 = 22 × 120 = 10.8 km/hr. 244

Second Method :
Here, d1 = 10, S1 = 12
d2 = 12, S2 = 10
 Average Speed = d1 + d2 d1 + d2 S1 S2

 = 10 + 12 10 + 12 12 10

 = 22 × 120 = 10.8 km/hrs. 244

##### Correct Option: B

Total distance = 10 + 12 = 22 km

 Total time = 10 + 12 12 10

 = 244 hours 120

 ∴  Required average speed = Total distance Total time

 = 22 244 120

 = 22 × 120 = 10.8 km/hr. 244

Second Method :
Here, d1 = 10, S1 = 12
d2 = 12, S2 = 10
 Average Speed = d1 + d2 d1 + d2 S1 S2

 = 10 + 12 10 + 12 12 10

 = 22 × 120 = 10.8 km/hrs. 244

1. A car moving in the morning fog passes a man walking at 4 km/h. in the same direction. The man can see the car for 3 minutes and visibility is upto a distance of 130 m. The speed of the car is :
1.  7 3 km. per hour 5
2.  6 3 km. per hour 5
3. 7 km. per hour
4. 5 km. per hour

1. Speed of car = x kmph.
Relative speed = (x – 4) kmph.

 Time = 3 minutes = 3 hours = 1 hours 60 20

Distance = 130 metre
 = 130 km. = 13 km. 1000 100

 ∴  Relative speed = Distance Time

 ⇒  x – 4 = 13 × 20 100

⇒  5x – 20 = 13
⇒  5x = 20 + 13 = 33
 ⇒  x = 33 = 6 3 kmph. 5 5

##### Correct Option: B

Speed of car = x kmph.
Relative speed = (x – 4) kmph.

 Time = 3 minutes = 3 hours = 1 hours 60 20

Distance = 130 metre
 = 130 km. = 13 km. 1000 100

 ∴  Relative speed = Distance Time

 ⇒  x – 4 = 13 × 20 100

⇒  5x – 20 = 13
⇒  5x = 20 + 13 = 33
 ⇒  x = 33 = 6 3 kmph. 5 5

1. A car covers a certain distance in 25 hours.
 If it reduces the speed by 1 th,the car covers 200 km. 5
less in that time. The speed of car is
1. 60 km./hr.
2. 30 km./hr.
3. 40 km./hr.
4. 50 km./hr.

1. Speed of car = x kmph.
∴  Distance = Speed × Time
= 25x km.
Case II,

 Speed of car = 4x kmph. 5

 Distance covered = 4x × 25 5

= 20x km.
According to the question,
25x – 20x = 200
⇒  5x = 200
 ⇒  x = 200 = 40 kmph. 5

##### Correct Option: C

Speed of car = x kmph.
∴  Distance = Speed × Time
= 25x km.
Case II,

 Speed of car = 4x kmph. 5

 Distance covered = 4x × 25 5

= 20x km.
According to the question,
25x – 20x = 200
⇒  5x = 200
 ⇒  x = 200 = 40 kmph. 5