## Speed, Time and Distance

#### Speed, Time and Distance

1. A hare sees a dog 100 metres away from her and scuds off in the opposite direction at a speed of 12 km per hr. A minute later the dog perceives her and chases her at a speed of 16 km per hr. How soon will the dog overtake the hare and at what distance from the spot when the hare took flight?
1. 900 metres
2. 950 metres
3. 1000 metres
4. 1100 metres

1. Let the hare at B sees that dog is at A.
∴  AB = 100 metres
Again, let C be the position of the hare when the dog sees her.
∴  AB = 100 metres
Again, let C be the position of the hare when the dog sees her.
∴  BC= the distance covered by the hare in 1 minute

 = 12 × 1000 × 1 = 200 metres 60

∴  AC = AB + BC
= 100 + 200 = 300 metres
Thus, hare has a start of 300 metres.
Now, the dog gains 16 – 12 = 4 kms
4000 metres in 1 hour i.e. 60 minutes
∴  The distance gained by dog in 1 minute
 = 4000 = 200 metres 60 3

 ∵ 200 metres is covered in 1 minute 3

∴  300 metres is covered in
 300 × 3 = 9 minutes 200 2

 Again the distance walked by hare in 9 minutes 2

 = 12000 × 9 = 900 metres 60 2

∴  Total distance from
B = 200 + 900 = 1100 metres.

##### Correct Option: D

Let the hare at B sees that dog is at A.
∴  AB = 100 metres
Again, let C be the position of the hare when the dog sees her.
∴  AB = 100 metres
Again, let C be the position of the hare when the dog sees her.
∴  BC= the distance covered by the hare in 1 minute

 = 12 × 1000 × 1 = 200 metres 60

∴  AC = AB + BC
= 100 + 200 = 300 metres
Thus, hare has a start of 300 metres.
Now, the dog gains 16 – 12 = 4 kms
4000 metres in 1 hour i.e. 60 minutes
∴  The distance gained by dog in 1 minute
 = 4000 = 200 metres 60 3

 ∵ 200 metres is covered in 1 minute 3

∴  300 metres is covered in
 300 × 3 = 9 minutes 200 2

 Again the distance walked by hare in 9 minutes 2

 = 12000 × 9 = 900 metres 60 2

∴  Total distance from
B = 200 + 900 = 1100 metres.

1. A monkey climbing up a greased pole ascends 12 metres and slips down 5 metres in alternate minutes. If the pole is 63 metres high, how long will it take him to reach the top?
1. 18 minutes
2. 16 minutes
3.  16 7 minutes 12
4. 18 minutes 20 seconds

1. In 1 minute the monkey climbs 12 metres but then he takes 1 minute to slip down 5
metres. So, at the end of 2 minutes the net ascending of the monkey is 12 – 5 = 7 metres.
So, to cover 63 metres the above

 process is repeated 63 = 9 7

times. Obviously, in 9 such happenings the monkey will slip 8 times, because on 9th time, it
will climb to the top. Thus, in climbing 8 times and slipping 8 times, he covers 8 × 7 = 56 metres.
Time taken to cover 56 metres
 = 56 × 2 = 16 minutes 7

Remaining distance
= 63 – 56 = 7 metres
Time taken to ascend 7 metres
 = 7 minutes 12

 ∴  Total time taken = 16 + 7 12

 = 16 7 minutes. 12

##### Correct Option: C

In 1 minute the monkey climbs 12 metres but then he takes 1 minute to slip down 5
metres. So, at the end of 2 minutes the net ascending of the monkey is 12 – 5 = 7 metres.
So, to cover 63 metres the above

 process is repeated 63 = 9 7

times. Obviously, in 9 such happenings the monkey will slip 8 times, because on 9th time, it
will climb to the top. Thus, in climbing 8 times and slipping 8 times, he covers 8 × 7 = 56 metres.
Time taken to cover 56 metres
 = 56 × 2 = 16 minutes 7

Remaining distance
= 63 – 56 = 7 metres
Time taken to ascend 7 metres
 = 7 minutes 12

 ∴  Total time taken = 16 + 7 12

 = 16 7 minutes. 12

1. Ravi can walk a certain distance in 40 days when he rests 9 hours a day. How long will he take to walk twice the distance, twice as fast and rest twice as long each day?
1. 80 days
2. 100 days
3. 90 days
4. 95 days

1. Working hours per day= 24 – 9 = 15 hrs.
Total working hours for 40 days
= 15 × 40 = 600 hrs.
On doubling the distance, the time required becomes twice but on walking twice as fast, the time required gets halved. Therefore, the two together cancel each other with respect to time required. Increasing rest to twice reduces walking hours per day to
24 – (2 × 9) = 6 hrs.
∴  Total number of days required to cover twice the distance, at twice speed with twice the rest.

 = 600 = 100 days 6

##### Correct Option: B

Working hours per day= 24 – 9 = 15 hrs.
Total working hours for 40 days
= 15 × 40 = 600 hrs.
On doubling the distance, the time required becomes twice but on walking twice as fast, the time required gets halved. Therefore, the two together cancel each other with respect to time required. Increasing rest to twice reduces walking hours per day to
24 – (2 × 9) = 6 hrs.
∴  Total number of days required to cover twice the distance, at twice speed with twice the rest.

 = 600 = 100 days 6

1. On increasing the speed of a train at the rate of 10 km per hr, 30 minutes is saved in a journey of 100 kms. Find the initial speed of train.
1. 40 kmph
2. 45 kmph
3. 42 kmph
4. 44 kmph

1. Let the original speed be x km/hr
then, increased speed
= (x + 10) km/hr
According to question,

 100 − 100 = 30 x x + 10 60

[ ∵  Original time − New time
 = 30 minute or 30 hr   ] 60

 ⇒  100 1 − 1 = 1 x x + 10 2

 ⇒ x + 10 − x = 1 x(x + 10) 200

⇒  10 × 200 = x (x + 10)
⇒  x2 + 10x – 2000 = 0
⇒  x2 + 50x – 40x – 2000 = 0
⇒  x (x + 50) – 40 (x + 50) = 0
⇒  x = – 50, 40
Speed can’t be negative.
Hence, Original speed = 40 kmph

##### Correct Option: A

Let the original speed be x km/hr
then, increased speed
= (x + 10) km/hr
According to question,

 100 − 100 = 30 x x + 10 60

[ ∵  Original time − New time
 = 30 minute or 30 hr   ] 60

 ⇒  100 1 − 1 = 1 x x + 10 2

 ⇒ x + 10 − x = 1 x(x + 10) 200

⇒  10 × 200 = x (x + 10)
⇒  x2 + 10x – 2000 = 0
⇒  x2 + 50x – 40x – 2000 = 0
⇒  x (x + 50) – 40 (x + 50) = 0
⇒  x = – 50, 40
Speed can’t be negative.
Hence, Original speed = 40 kmph

1. A man travels 400 kms in 4 hours partly by air and partly by train. If he had travelled all the way by air,
 he would have saved 4 of the time he was in train 5
and would have arrived his destination 2 hours early. Find the distance he travelled by train.
1. 95 km.
2. 85 km.
3. 90 km.
4. 100 km.

1. Obviously, 4/5 of total time in train = 2 hours

 ∴  Total time in train = 5 × 2 = 5 hours 4 2

Total time to cover 400 km is 4 hours
∴  Time spent in travelling by air
 = 4 − 5 = 8 − 5 = 3 hours 2 2 2

If 400 kms is travelled by air, then time taken = 2 hours
∴  In 2 hours, distance covered by air = 400 kms
 In 3/2 hours distance covered = 400 × 3 = 300 kms 2 2

Distance covered by the train
= 400 – 300 = 100 kms.

##### Correct Option: D

Obviously, 4/5 of total time in train = 2 hours

 ∴  Total time in train = 5 × 2 = 5 hours 4 2

Total time to cover 400 km is 4 hours
∴  Time spent in travelling by air
 = 4 − 5 = 8 − 5 = 3 hours 2 2 2

If 400 kms is travelled by air, then time taken = 2 hours
∴  In 2 hours, distance covered by air = 400 kms
 In 3/2 hours distance covered = 400 × 3 = 300 kms 2 2

Distance covered by the train
= 400 – 300 = 100 kms.