## Speed, Time and Distance

#### Speed, Time and Distance

1. A man takes 6 hours 15 minutes in walking a distance and riding back to the starting place. He could walk both ways in 7 hours 45 minutes. The time taken by him to ride both ways, is
1. 4 hours
2. 4 hours 30 minutes
3. 4 hours 45 minutes
4. 5 hours

1. Time taken in walking both ways = 7 hours 45 minutes   ....(i)
Time taken in walking one way and riding back = 6 hours 15 minutes   ....(ii)
By equation (ii) × 2 – (i), we have Time taken by the man to ride both ways
= 12 hours 30 minutes – 7 hours 45 minutes
= 4 hours 45 minutes

##### Correct Option: C

Time taken in walking both ways = 7 hours 45 minutes   ....(i)
Time taken in walking one way and riding back = 6 hours 15 minutes   ....(ii)
By equation (ii) × 2 – (i), we have Time taken by the man to ride both ways
= 12 hours 30 minutes – 7 hours 45 minutes
= 4 hours 45 minutes

1. In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed (in km/hr) is
1. 5
2. 6
3. 6.25
4. 7.5

1. Abhay’s speed = x kmph
Sameer’s speed = y kmph

 ∴ 30 − 30 = 2   ...(i) x y

 and, 30 − 30 = 1   ...(ii) y 2x

 30 − 30 = 3 x 2x

 ⇒ 60 − 30 = 3 2x

 ⇒ 30 = 3 ⇒ 6x = 30 2x

⇒  x = 5 kmph

##### Correct Option: A

Abhay’s speed = x kmph
Sameer’s speed = y kmph

 ∴ 30 − 30 = 2   ...(i) x y

 and, 30 − 30 = 1   ...(ii) y 2x

 30 − 30 = 3 x 2x

 ⇒ 60 − 30 = 3 2x

 ⇒ 30 = 3 ⇒ 6x = 30 2x

⇒  x = 5 kmph

1. A and B started at the same time from the same place for a certain destination.
 B walking at 5 of A’s speed reached the destination 6
1 hour 15 minutes after A. B reached the destination in
1. 6 hours 45 minutes
2. 7 hours 15 minutes
3. 7 hours 30 minutes
4. 8 hours 15 minutes

1.  1 − 5 of time taken by B 6

=1 hour 15 minutes
∴  Time taken by B
= 1 hour 15 minutes × 6
=7 hours 30 minutes

##### Correct Option: C

 1 − 5 of time taken by B 6

=1 hour 15 minutes
∴  Time taken by B
= 1 hour 15 minutes × 6
=7 hours 30 minutes

1. Ram arrives at a Bank 15 minutes earlier than scheduled time if he drives his car at 42 km/hr. If he drives car at 35 km/hr he arrives 5 minutes late. The distance of the Bank from his starting point is
1. 70 km
2. 210 km
3. 72 km
4. 60 km

1. Let the required distance be x km.
Difference of time = 15 + 5 = 20 minutes

 = 1 hour 3

According to the question,
 x − x = 1 ⇒ 6x − 5x = 1 35 42 3 210 3

 ⇒ x = 1 210 3

 ⇒   x = 210 = 70 km. 3

##### Correct Option: A

Let the required distance be x km.
Difference of time = 15 + 5 = 20 minutes

 = 1 hour 3

According to the question,
 x − x = 1 ⇒ 6x − 5x = 1 35 42 3 210 3

 ⇒ x = 1 210 3

 ⇒   x = 210 = 70 km. 3

1. Two guns are fired from the same place at an interval of 6 minutes. A person approaching the place observes that 5 minutes 52 seconds have elapsed between the hearing of the sound of the two guns. If the velocity of the sound is 330 m/sec, the man was approaching that place at what speed (in km/hr) ?
1. 24
2. 27
3. 30
4. 36

1. Difference of time
= 6 min. – 5 min. 52 sec.
= 8 seconds
Distance covered by man in 5 min.52 seconds
= Distance covered by sound in 8 seconds
= 330 × 8 = 2640 m.

 ∴ Speed of man = 2640 m 5 min. 52 sec.

 = 2640 m/sec 352

 = 2640 × 18 kmph 352 5

= 27 kmph

##### Correct Option: B

Difference of time
= 6 min. – 5 min. 52 sec.
= 8 seconds
Distance covered by man in 5 min.52 seconds
= Distance covered by sound in 8 seconds
= 330 × 8 = 2640 m.

 ∴ Speed of man = 2640 m 5 min. 52 sec.

 = 2640 m/sec 352

 = 2640 × 18 kmph 352 5

= 27 kmph