## Speed, Time and Distance

#### Speed, Time and Distance

1. When Alisha goes by car at 50 kmph, she reaches her office 5 minutes late. But when she takes her motorbike, she reaches 3 minutes early. If her office is 25 kms away, what is the approximate average speed at which she rides her motorbike ?
1. 68 kmph
2. 62 kmph
3. 58 kmph
4. 52 kmph

1. Difference of time = 5 + 3 = 8 minutes

 = 8 hour = 2 hour 60 15

If the speed of motorbike be x kmph, then
 25 − 25 = 2 50 x 15

 ⇒ 25 = 1 − 2 x 2 15

 ⇒ 25 = 15 − 4 = 11 x 30 30

⇒ 11x = 25 × 30
 ⇒ x = 25 × 30 11

 = 750 = 68.18 kmph 11

≈ 68 kmph

##### Correct Option: A

Difference of time = 5 + 3 = 8 minutes

 = 8 hour = 2 hour 60 15

If the speed of motorbike be x kmph, then
 25 − 25 = 2 50 x 15

 ⇒ 25 = 1 − 2 x 2 15

 ⇒ 25 = 15 − 4 = 11 x 30 30

⇒ 11x = 25 × 30
 ⇒ x = 25 × 30 11

 = 750 = 68.18 kmph 11

≈ 68 kmph

1. A man covers a total distance of 100 km on bicycle. For the first 2 hours, the speed was 20 km/hr and for the rest of the journey, it came down to 10 km/hr. The average speed will be
1.  12 1 km/hr 2
2. 13 km/hr
3.  15 1 km/hr 8
4. 20 km/hr

1. Distance covered in first 2 hours
= 2 × 20 = 40 km.
Remaining distance
= 100 – 40 = 60 km.
Time taken in covering 60 km at 10 kmph

 = 60 = 6 hours 10

 ∴  Required average speed = Total distance Total Time

 = 100 kmph 2 + 6

 = 100 kmph 8

 = 25 kmph 2

 = 12 1 kmph 2

##### Correct Option: A

Distance covered in first 2 hours
= 2 × 20 = 40 km.
Remaining distance
= 100 – 40 = 60 km.
Time taken in covering 60 km at 10 kmph

 = 60 = 6 hours 10

 ∴  Required average speed = Total distance Total Time

 = 100 kmph 2 + 6

 = 100 kmph 8

 = 25 kmph 2

 = 12 1 kmph 2

1. A train travels 500 m in first minute. In the next 4 minutes, it travels in each minute 125 m more than that in the previous minute. The average speed per hour of the train during those 5 minutes will be
1. 30 km/hr
2. 45 km/hr
3. 50 km/hr
4. 55 km/hr

1. Total distance covered by train in 5 minutes
= (500 + 625 + 750 + 875 + 1000) metre = 3750 metre
= 3.75 km.

 Time = 5 minutes = 5 hour 60

 = 1 hour 12

 Speed of train = Distance Time

 = 3.75 kmph (1/12)

= (3.75 × 12) kmph
= 45 kmph

##### Correct Option: B

Total distance covered by train in 5 minutes
= (500 + 625 + 750 + 875 + 1000) metre = 3750 metre
= 3.75 km.

 Time = 5 minutes = 5 hour 60

 = 1 hour 12

 Speed of train = Distance Time

 = 3.75 kmph (1/12)

= (3.75 × 12) kmph
= 45 kmph

1. A train runs at an average speed of 75 km/hr. If the distance to be covered is 1050 kms, how long will the train take to cover it ?
1. 13 hrs
2. 12 hrs
3. 15 hrs
4. 14 hrs

1.  Time = Distance Speed

 = 1050 = 14 hours 75

##### Correct Option: D

 Time = Distance Speed

 = 1050 = 14 hours 75

1. A man walks from his house at an average speed of 5 km per hour and reaches his office 6 minutes late. If he walks at an average speed of 6 km/h he reaches 2 minutes early. The distance of the office from his house is
1. 6 km
2. 9 km
3. 12 km
4. 4 km

1. Required distance of office from house = x km. (let)

 Time = Distance Speed

∴  According to the question,
 x − x = 6 + 2 = 2 5 6 60 15

 ⇒ 6x − 5x 30

 = 2 15

 ⇒ x = 2 30 15

 ⇒ x = 2 × 30 = 4 km. 15

Second Method :
Here, S1 = 5, t1 = 6
S2 = 6, t2 = 2
 Distance = (S1 × S2)(t1 + t2) S2 − S1

 = (5 × 6)(6 + 2) 6 − 5

 = 30 × 8 = 4 km. 60

##### Correct Option: D

Required distance of office from house = x km. (let)

 Time = Distance Speed

∴  According to the question,
 x − x = 6 + 2 = 2 5 6 60 15

 ⇒ 6x − 5x 30

 = 2 15

 ⇒ x = 2 30 15

 ⇒ x = 2 × 30 = 4 km. 15

Second Method :
Here, S1 = 5, t1 = 6
S2 = 6, t2 = 2
 Distance = (S1 × S2)(t1 + t2) S2 − S1

 = (5 × 6)(6 + 2) 6 − 5

 = 30 × 8 = 4 km. 60