## Speed, Time and Distance

#### Speed, Time and Distance

1. A car travels from A to B at the rate of 40 km/h and returns from B to A at the rate of 60 km/h. Its average speed during the whole journey is
1. 48 km/h
2. 50 km/h
3. 45 km/h
4. 60 km/h

1. Here, distance is same.

 ∴  Average speed = 2xy x + y

 = 2 × 40 × 60 kmph. 40 + 60

 = 2 × 40 × 60 kmph. 100

= 48 kmph.

##### Correct Option: A

Here, distance is same.

 ∴  Average speed = 2xy x + y

 = 2 × 40 × 60 kmph. 40 + 60

 = 2 × 40 × 60 kmph. 100

= 48 kmph.

1. Gautam travels 160 kms at 32 kmph and returns at 40 kmph. Then his average speed is
1. 72 kmph
2. 71.11 kmph
3. 36 kmph
4. 35.55 kmph

1. Here, distances are equal.

 ∴  Average speed = 2xy kmph. x + y

 = 2 × 32 × 40 kmph. 32 + 40

 = 2 × 32 × 40 kmph. 72

 = 320 kmph. = 35.55 kmph. 9

##### Correct Option: D

Here, distances are equal.

 ∴  Average speed = 2xy kmph. x + y

 = 2 × 32 × 40 kmph. 32 + 40

 = 2 × 32 × 40 kmph. 72

 = 320 kmph. = 35.55 kmph. 9

1. Durga walks 5 km from her home to school in 60 minutes, then bicycles back to home along the same route at 15 km per hour. Her sister Smriti makes the same round trip, but does so at half of Durga’s average speed. How much time does Smriti spend on her round trip ?
1. 120 minutes
2. 40 minutes
3. 160 minutes
4. 80 minutes

1.  Durga’s average speed = 2xy kmph. x + y
 = 2 × 5 × 15 kmph 20

 = 15 kmph 2

Distance of School = 5 km.
 ∴  Required time = 2 5 hours 15/4

 = 2 × 5 × 4 hours 15

 = 8 hours 3

 = 8 × 60 minutes 3

= 160 minutes

##### Correct Option: C

 Durga’s average speed = 2xy kmph. x + y
 = 2 × 5 × 15 kmph 20

 = 15 kmph 2

Distance of School = 5 km.
 ∴  Required time = 2 5 hours 15/4

 = 2 × 5 × 4 hours 15

 = 8 hours 3

 = 8 × 60 minutes 3

= 160 minutes

1.  A car completed a journey of 400 km in 12 1 hrs. 2
 The first 3 th of the journey was done at 30 km/hr. 4
Calculate the speed for the rest of the journey.
1. 45 km/hr
2. 25 km/hr
3. 40 km/hr
4. 30 km/hr

1. Total distance covered = 400 km.

 Total time = 25 hours 2

 ∴ 3 th of total journey 4

 = 3 × 400 = 300 km. 4

 Time taken = Distance Speed

 = 300 = 10 hours 30

 Remaining time = 25 − 2 2

 = 25 − 20 = 5 hours 2 2

Remaining distance = 100 km.
 ∴  Required speed of car = 100 5 2

 = 100 × 2 = 40 kmph. 5

##### Correct Option: C

Total distance covered = 400 km.

 Total time = 25 hours 2

 ∴ 3 th of total journey 4

 = 3 × 400 = 300 km. 4

 Time taken = Distance Speed

 = 300 = 10 hours 30

 Remaining time = 25 − 2 2

 = 25 − 20 = 5 hours 2 2

Remaining distance = 100 km.
 ∴  Required speed of car = 100 5 2

 = 100 × 2 = 40 kmph. 5

1. A man goes to a place on bicycle at speed of 16 km/hr and comes back at lower speed. If the average speed is 6.4 km/hr in total journey, then the return speed (in km/hr) is :
1. 10
2. 8
3. 6
4. 4

1. Let the speed of cyclist while returning be x kmph.

 ∴  Average speed = 2 × 16 × x 16 + x

 ⇒  6.4 = 32x 16 + x

⇒  6.4 × 16 + 6.4x = 32x
⇒  32x – 6.4x = 6.4 × 16
⇒  25.6x = 6.4 × 16
 ⇒  x = 6.4 × 16 25.6

= 4 kmph.

##### Correct Option: D

Let the speed of cyclist while returning be x kmph.

 ∴  Average speed = 2 × 16 × x 16 + x

 ⇒  6.4 = 32x 16 + x

⇒  6.4 × 16 + 6.4x = 32x
⇒  32x – 6.4x = 6.4 × 16
⇒  25.6x = 6.4 × 16
 ⇒  x = 6.4 × 16 25.6

= 4 kmph.