## Speed, Time and Distance

#### Speed, Time and Distance

1.  Walking at 3 of his usual speed, a man reaches 4
his office 20 minutes late. Then his usual time for walking to his office is :
1. 1 hour
2. 30 minutes
3. 45 minutes
4. 40 minutes

1. Usual time = x minutes

 New time = 4x minutes 3 ∵  Speed ∝ 1 Time

According to the question,
 4x − x = 20 3

 ⇒ x = 20 3

⇒  x = 60 minutes i.e. 1 hour.

##### Correct Option: A

Usual time = x minutes

 New time = 4x minutes 3 ∵  Speed ∝ 1 Time

According to the question,
 4x − x = 20 3

 ⇒ x = 20 3

⇒  x = 60 minutes i.e. 1 hour.

1. Sarthak completed a marathon in 4 hours and 35 minutes. The marathon consisted of a 10 km run followed by 20 km cycle ride and the remaining distance again a run. He ran the first stage at 6 km/hr and then cycled at 16 km/hr. How much distance did Sarthak cover in total, if his speed in the last run was just half that of his first run?
1. 5 km.
2. 35 km.
3. 40 km.
4. 45 km.

1. Let the total distance be x km.

 Time = Distance Speed

According to the question,
 10 + 20 + x − 30 = 4 35 6 16 3 60

 = 4 7 12

 ⇒ 5 + 5 + x − 10 = 55 3 4 3 12

 ⇒ x + 5 + 5 − 10 = 55 3 3 4 12

 ⇒ x + 20 + 15 − 120 = 55 3 12 12

 ⇒ x − 85 = 55 3 12 12

 ⇒ x = 85 + 55 = 140 3 12 12 12

 ⇒ x = 140 × 3 = 35 km. 12

##### Correct Option: B

Let the total distance be x km.

 Time = Distance Speed

According to the question,
 10 + 20 + x − 30 = 4 35 6 16 3 60

 = 4 7 12

 ⇒ 5 + 5 + x − 10 = 55 3 4 3 12

 ⇒ x + 5 + 5 − 10 = 55 3 3 4 12

 ⇒ x + 20 + 15 − 120 = 55 3 12 12

 ⇒ x − 85 = 55 3 12 12

 ⇒ x = 85 + 55 = 140 3 12 12 12

 ⇒ x = 140 × 3 = 35 km. 12

1. Walking at the rate of 4 kmph a man covers certain distance in 2 hrs 45 min. Running at a speed of 16.5 kmph the man will cover the same distance in how many minutes ?
1. 50 min.
2. 35 min.
3. 40 min.
4. 45 min.

1. 2 hours 45 minutes

 = 2 + 45 hours 60

 = 2 + 3 hours 4

 = 11 hours 4

∴  Distance = Speed × Time
 = 4 × 11 = 11 km. 4

∴  Time taken in covering 11 km at 16.5 kmph
 = 11 hour 16.5

 = 11 × 10 × 60 minutes 165

= 40 minutes

##### Correct Option: C

2 hours 45 minutes

 = 2 + 45 hours 60

 = 2 + 3 hours 4

 = 11 hours 4

∴  Distance = Speed × Time
 = 4 × 11 = 11 km. 4

∴  Time taken in covering 11 km at 16.5 kmph
 = 11 hour 16.5

 = 11 × 10 × 60 minutes 165

= 40 minutes

1. A is twice as fast as B, and B is thrice as fast as C is. The journey covered by
 C in 1 1 hours will be covered by A in 2
1. 15 minutes
2. 30 minutes
3. 1 hour
4. 10 minutes

1. Time taken by C = t hours

 ∴   Time taken by B = t hours 3

 and time taken by A = t hours 6

 Here, t = 3 hours 2

 ∴  Required time taken by A = 3 hour 2 6

 = 1 hour 4

 = 1 × 60 minutes 4

= 15 minutes

##### Correct Option: A

Time taken by C = t hours

 ∴   Time taken by B = t hours 3

 and time taken by A = t hours 6

 Here, t = 3 hours 2

 ∴  Required time taken by A = 3 hour 2 6

 = 1 hour 4

 = 1 × 60 minutes 4

= 15 minutes

1. A jeep is chasing a car which is 5km ahead. Their respective speed are 90 km/hr and 75 km/hr. After how many minutes will the jeep catch the car ?
1. 18 min.
2. 20 min.
3. 24 min.
4. 25 min.

1. Relative speed
= 95 – 75 = 15 kmph

 Required time = Distance Relative speed

 = 5 hours 15

 = 5 × 60 minutes 15

= 20 minutes

##### Correct Option: B

Relative speed
= 95 – 75 = 15 kmph

 Required time = Distance Relative speed

 = 5 hours 15

 = 5 × 60 minutes 15

= 20 minutes