## Speed, Time and Distance

#### Speed, Time and Distance

1.  By walking 5 of usual speed a student 3
reaches school 20 minutes earlier. Find his usual time.
1. 45 minutes
2. 50 minutes
3. 60 minutes
4. None of these

1. 5/3 of usual speed means 3/5 of usual time as he reaches earlier.

 ∴ 3 usual time + 20 minutes = Usual time 5

 20 minutes = 1 − 3 usual time 5

 = 2 usual time 5

 ∴   Usual time = 20 × 5 = 50 minutes. 2

##### Correct Option: B

5/3 of usual speed means 3/5 of usual time as he reaches earlier.

 ∴ 3 usual time + 20 minutes = Usual time 5

 20 minutes = 1 − 3 usual time 5

 = 2 usual time 5

 ∴   Usual time = 20 × 5 = 50 minutes. 2

1.  Walking 3 of my usual speed, a late 4
is marked on my cards by 10 minutes. Find my usual time.
1. 30 minutes
2. 35 minutes
3. 32 minutes
4. 36 minutes

1. Since I walk at 3/4 of my usual speed the time taken is 4/3 of my usual time.
[∵  the speed and time are in the inverse ratio]

 ∴ 4 of usual time 3

= Usual time + Time I reach late
 ∴ 1 of usual time 3

= 10 minutes
∴  Usual time
= 10 × 3 = 30 minutes.

##### Correct Option: A

Since I walk at 3/4 of my usual speed the time taken is 4/3 of my usual time.
[∵  the speed and time are in the inverse ratio]

 ∴ 4 of usual time 3

= Usual time + Time I reach late
 ∴ 1 of usual time 3

= 10 minutes
∴  Usual time
= 10 × 3 = 30 minutes.

1. A man has to reach a place 40 kms away. He walks at the rate of 4 km per hr. for the first 16 kms and then he hires a rickshaw for the rest of the journey. However if he had travelled by the rickshaw for the first 16 kms and the remaining distance on foot at 4 km per hr, he would have taken an hour longer to complete the journey. Find the speed of rickshaw.
1. 6.5 kmph
2. 7.5 kmph
3. 6 kmph
4. 8 kmph

1. Let the speed of Rickshaw be 'x ' .
Then, time taken to cover 16 km on foot and 24 km on Rikshaw

 = 16 + 24 hrs 4 x

and time taken to travel 24 km on foot & 16 km on Rikshaw
 = 16 + 24 hrs x 4

According to question,
 = 16 + 24 + 1 = 16 + 24 4 x x 4

 ⇒ 5 + 24 = 16 + 6 x x

 ⇒ 24 − 16 = 1 x

⇒  x = 8 km/hr

##### Correct Option: D

Let the speed of Rickshaw be 'x ' .
Then, time taken to cover 16 km on foot and 24 km on Rikshaw

 = 16 + 24 hrs 4 x

and time taken to travel 24 km on foot & 16 km on Rikshaw
 = 16 + 24 hrs x 4

According to question,
 = 16 + 24 + 1 = 16 + 24 4 x x 4

 ⇒ 5 + 24 = 16 + 6 x x

 ⇒ 24 − 16 = 1 x

⇒  x = 8 km/hr

1. If a boy walks from his house to school at the rate of 4 km per hr, he reaches the school 10 minutes earlier than the scheduled time. However if he walks at the rate of 3 km per hr, he reaches 10 minutes late. Find the distance of his school from his house.
1. 3.5 km
2. 3 km
3. 4 km
4. 4.5 km

1. Let the distance be x kms.
∴  Time taken at 4 km per hr. t1

 = x hrs. 4

Time taken at 3 km per hr.t2
 = x hrs. 3

Difference in timings
= 10 + 10 = 20 minutes
 or 20 = 1 hour 60 3

 ∴ x − x = 1 3 4 3

 ⇒ 4x − 3x = 1 12 3

 ⇒ x = 1 12 3

∴  x = 4 km.
Hence the required distance
= 4 kms.

##### Correct Option: C

Let the distance be x kms.
∴  Time taken at 4 km per hr. t1

 = x hrs. 4

Time taken at 3 km per hr.t2
 = x hrs. 3

Difference in timings
= 10 + 10 = 20 minutes
 or 20 = 1 hour 60 3

 ∴ x − x = 1 3 4 3

 ⇒ 4x − 3x = 1 12 3

 ⇒ x = 1 12 3

∴  x = 4 km.
Hence the required distance
= 4 kms.

1. A car can finish a certain journey in 10 hours at a speed of 48 km per hr. In order to cover the same distance in 8 hours, how much the speed be increased by ?
1. 10 kmph
2. 12 kmph
3. 14 kmph
4. 15 kmph

1. Time = 10 hours,
Speed = 48 km per hr.
∴  Distance = Speed × Time
= 48 × 10 = 480 km
Now, this distance of 480 kms is to be covered in 8 hours.
Hence, the required Speed

 = Distance = 480 New time 8

= 60 km per hr.
∴  Increase in speed
= 60 – 48 = 12 km per hr.

##### Correct Option: B

Time = 10 hours,
Speed = 48 km per hr.
∴  Distance = Speed × Time
= 48 × 10 = 480 km
Now, this distance of 480 kms is to be covered in 8 hours.
Hence, the required Speed

 = Distance = 480 New time 8

= 60 km per hr.
∴  Increase in speed
= 60 – 48 = 12 km per hr.