## Speed, Time and Distance

#### Speed, Time and Distance

1. A man completes 30 km of a journey at the speed of 6 km/hr and the remaining 40 km of the journey in 5 hours. His average speed for the whole journey is
1. 7 km/hr
2.  6 4 km/hr 11
3. 8 km/hr
4. 7.5 km/hr

1.  Time taken to cover 30km at 6 kmph = 30 = 5 hours 6

Time taken to cover 40 km = 5 hours
 ∴  Average speed = Total distance Time taken

 = 30 + 40 10

 = 70 = 7 kmph 10

##### Correct Option: A

 Time taken to cover 30km at 6 kmph = 30 = 5 hours 6

Time taken to cover 40 km = 5 hours
 ∴  Average speed = Total distance Time taken

 = 30 + 40 10

 = 70 = 7 kmph 10

1. One third of a certain journey is covered at the rate of 25 km/hour, one-fourth at the rate of 30 km/hour and the rest at 50 km/hour. The average speed for the whole journey is
1. 35 km/hour
2.  33 1 km/hr 3
3. 30 km/hour
4.  37 1 km/hr 12

1. Let the total distance be x km.

 Total time = x x 5x 3 + 4 + 12 25 30 50

 = x + x + x 75 120 120

 = x + x 75 60

 = 4x + 5x = 3x hours 300 100

 ∴  Average speed = Total distance Time taken

 = x 3x 100

 = 100 = 33 1 kmph 3 3

Second Method :
Here, x = 3, u = 25, y = 4, v = 30
 z = 12 , w = 50 5

 Average Speed = 1 1 + 1 + 1 xu yv zw

 = 1 1 + 1 + 1 3 × 25 4 × 30 (12/5) × 50

 = 1 1 + 1 + 1 75 120 120

 = 1 1 + 1 75 60

 = 1 4 + 5 300

 = 300 = 100 9 3

 = 33 1 km/hr. 3

##### Correct Option: B

Let the total distance be x km.

 Total time = x x 5x 3 + 4 + 12 25 30 50

 = x + x + x 75 120 120

 = x + x 75 60

 = 4x + 5x = 3x hours 300 100

 ∴  Average speed = Total distance Time taken

 = x 3x 100

 = 100 = 33 1 kmph 3 3

Second Method :
Here, x = 3, u = 25, y = 4, v = 30
 z = 12 , w = 50 5

 Average Speed = 1 1 + 1 + 1 xu yv zw

 = 1 1 + 1 + 1 3 × 25 4 × 30 (12/5) × 50

 = 1 1 + 1 + 1 75 120 120

 = 1 1 + 1 75 60

 = 1 4 + 5 300

 = 300 = 100 9 3

 = 33 1 km/hr. 3

1. A man goes from a place A to B at a speed of 12 km/hr and returns from B to A at a speed of 18 km/hr. The average speed for the whole journey is
1.  14 2 km/hr 5
2. 15 km/hr
3.  15 1 km/hr 2
4. 16 km/hr

1.  Average speed = 2xy kmph x + y

 = 2 × 12 × 18 kmph 12 + 18

 = 2 × 12 × 18 kmph 30

 = 14 2 kmph 5

##### Correct Option: B

 Average speed = 2xy kmph x + y

 = 2 × 12 × 18 kmph 12 + 18

 = 2 × 12 × 18 kmph 30

 = 14 2 kmph 5

1. A man goes from Mysore to Bangalore at a uniform speed of 40 km/hr and comes back to
Mysore at a uniform speed of 60 km/hr. His average speed for the whole journey is
1. 48 km/hr
2. 50 km/hr
3. 54 km/hr
4. 55 km/hr

1.  Average speed = 2xy kmph x + y

 = 2 × 40 × 60 kmph 40 + 60

= 48 kmph

##### Correct Option: A

 Average speed = 2xy kmph x + y

 = 2 × 40 × 60 kmph 40 + 60

= 48 kmph

1. A person went from A to B at an average speed of x km/hr and returned from B to A at an average speed of y km/hr. What was his average speed during the total journey ?
1.  x + y 2xy
2.  2xy x + y
3.  2 x + y
4.  1 + 1 x y

1.  Required average speed = 2xy kmph x + y

[Since, can be given as corollary If the distance between A and B be z units, then
 Average speed = Total distance Time taken

 = z + z z + z x y

 = 2 1 + 1 x y

 = 2 x + y xy

 = 2xy x + y

##### Correct Option: B

 Required average speed = 2xy kmph x + y

[Since, can be given as corollary If the distance between A and B be z units, then
 Average speed = Total distance Time taken

 = z + z z + z x y

 = 2 1 + 1 x y

 = 2 x + y xy

 = 2xy x + y