## Speed, Time and Distance

#### Speed, Time and Distance

1. A student goes to school at the
 rate of 5 km/hr and reaches 6 minutes late. 2
If he travels at the speed of 3 km/hr, he reaches 10 minutes earlier. The distance of the school is
1. 45 km
2. 20 km
3. 10 km
4. 4 km

1. Distance of school = x km
Difference of time

 = 16 minutes = 16 hour 60

 ∴ x − x = 16 5/2 3 60

 ⇒ 2x − x = 4 5 3 15

 ⇒ 6x − 5x = 4 15 15

 ⇒ x = 4 15 15

 ⇒ x = 4 × 15 = 4km 15

Second Method :
 Here, S1 = 5 ,t1 = 6 2

S2 = 3, t2 = 10
 Distance = (S1 × S2)(t1 + t2) S1 − S2

 = 5 × 3(6 + 10) 2 3 - 5 2

 = 15 × 16 km = 4 km. 60

##### Correct Option: D

Distance of school = x km
Difference of time

 = 16 minutes = 16 hour 60

 ∴ x − x = 16 5/2 3 60

 ⇒ 2x − x = 4 5 3 15

 ⇒ 6x − 5x = 4 15 15

 ⇒ x = 4 15 15

 ⇒ x = 4 × 15 = 4km 15

Second Method :
 Here, S1 = 5 ,t1 = 6 2

S2 = 3, t2 = 10
 Distance = (S1 × S2)(t1 + t2) S1 − S2

 = 5 × 3(6 + 10) 2 3 - 5 2

 = 15 × 16 km = 4 km. 60

1. A truck travels at 90 km/hr for
 the first 1 1 hours. After that it travels at 70 km/hr. 2
Find the time taken by the truck to travel 310 kilometres.
1. 2.5 hrs
2. 3 hrs
3. 3.5 hrs
4. 4 hrs

1.  Distance covered by truck in 3 hours 2

= Speed × Time
 = 90 × 3 = 135 km 2

Remaining distance
= 310 – 135 = 175 km
∴  Time taken at 70 kmph
 = 175 = 2.5 hours 70

∴  Total time = 1.5 + 2.5 = 4 hours

##### Correct Option: D

 Distance covered by truck in 3 hours 2

= Speed × Time
 = 90 × 3 = 135 km 2

Remaining distance
= 310 – 135 = 175 km
∴  Time taken at 70 kmph
 = 175 = 2.5 hours 70

∴  Total time = 1.5 + 2.5 = 4 hours

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. 20 minutes
3. 30 minutes
4. 1 hour

1. Speed of B = x kmph (let)
Speed of A = 2x kmph

 Speed of C = x kmph 3

 ∴ Speed of A = 2x = 6 Speed of C (x/3)

 ∴  Required time = 1 of 3 hours 6 2

 = 1 hour = 15 minutes 4

##### Correct Option: A

Speed of B = x kmph (let)
Speed of A = 2x kmph

 Speed of C = x kmph 3

 ∴ Speed of A = 2x = 6 Speed of C (x/3)

 ∴  Required time = 1 of 3 hours 6 2

 = 1 hour = 15 minutes 4

1. Motor-cyclist P started his journey at a speed of 30 km/hr. After 30 minutes, motor-cyclist Q
started from the same place but with a speed of 40 km/hr. How much time (in hours) will Q take to overtake P ?
1. 1
2.  3 2
3.  3 8
4. 2

1. Distance covered by motor cyclist P in 30 minutes

 = 30 × 1 = 15 km 2

Relative speed
= 40 – 30 = 10 kmph
∴  Required speed = Time taken to cover is km at 10 kmph
 = 15 = 3 hour 10 2

##### Correct Option: B

Distance covered by motor cyclist P in 30 minutes

 = 30 × 1 = 15 km 2

Relative speed
= 40 – 30 = 10 kmph
∴  Required speed = Time taken to cover is km at 10 kmph
 = 15 = 3 hour 10 2

1. A train covers a distance of 10 km in 12 minutes. If its speed is decreased by 5 km/hr, the time taken by it to cover the same distance is equal to
1. 40 minutes
2.  40 minutes 3
3. 20 minutes
4. 15 minutes

1. Time = 12 minutes

 = 12 hour = 1 hour 60 5

 Speed of train = 10 1 5

= 50 kmph
New speed = 50 – 5 = 45 kmph
 ∴  Required time = Distance Speed

 = 10 = 2 hour 45 9

 = 2 × 60 minutes 9

 = 40 minutes 3

Second Method :
 Here, S1 = 10 km/min 12

 = 10 × 60km/hr 12

 = 50 km/hr, t1 = 12 = 1 hr 60 5

S2 = 45 km/hr, t2 = ?
S1t1 = S2t2
 50 × 1 = 45 × t2 5
 t2 = 10 × 60 min 45

 = 40 min 3

##### Correct Option: B

Time = 12 minutes

 = 12 hour = 1 hour 60 5

 Speed of train = 10 1 5

= 50 kmph
New speed = 50 – 5 = 45 kmph
 ∴  Required time = Distance Speed

 = 10 = 2 hour 45 9

 = 2 × 60 minutes 9

 = 40 minutes 3

Second Method :
 Here, S1 = 10 km/min 12

 = 10 × 60km/hr 12

 = 50 km/hr, t1 = 12 = 1 hr 60 5

S2 = 45 km/hr, t2 = ?
S1t1 = S2t2
 50 × 1 = 45 × t2 5
 t2 = 10 × 60 min 45

 = 40 min 3