## Speed, Time and Distance

#### Speed, Time and Distance

1. A car can finish a certain journey in 10 hours at the speed of 42 kmph. In order to cover the same distance in 7 hours, the speed of the car (km/h) must be increased by :
1. 12
2. 15
3. 18
4. 24

1. Distance covered by car = 42 × 10 = 420 km.
New time = 7 hours

 ∴  Required speed = 420 = 60 kmph. 7

∴  Required increase
= (60 – 42) kmph
= 18 kmph

##### Correct Option: C

Distance covered by car = 42 × 10 = 420 km.
New time = 7 hours

 ∴  Required speed = 420 = 60 kmph. 7

∴  Required increase
= (60 – 42) kmph
= 18 kmph

1. A man travels for 5 hours 15 minutes. If he covers the first half of the journey at 60 km/h and rest at 45 km/h. Find the total distance travelled by him.
1.  1028 6 km. 7
2. 189 km.
3. 378 km.
4. 270 km.

1. Let the distance covered be 2x km.

 Time = Distance Speed

According to the question,
 x + x = 5 15 = 1 60 45 60 4

 ⇒ 3x + 4x = 21 180 4

 ⇒ 7x = 21 × 180 4

 ⇒  x = 21 × 180 = 135 km. 4 × 7

∴  Length of total journey
= 2 × 135 = 270 km.

##### Correct Option: D

Let the distance covered be 2x km.

 Time = Distance Speed

According to the question,
 x + x = 5 15 = 1 60 45 60 4

 ⇒ 3x + 4x = 21 180 4

 ⇒ 7x = 21 × 180 4

 ⇒  x = 21 × 180 = 135 km. 4 × 7

∴  Length of total journey
= 2 × 135 = 270 km.

1. A student goes to school at the
 rate of 2 1 km/hr and reaches 6 minutes late. 2
If he travels at the speed of 3 km/hr. he is 10 minutes early. What is the distance to the school?
1. 4 km
2.  3 1 km 2
3. 1 km
4.  3 1 km 4

1. Let the distance of school be x km.
Difference of time = 6 + 10

 = 16 minutes = 16 hour 60

 = 4 hour 15

 Time = Distance Speed

 ∴ x − x = 4 5/2 3 15

 ⇒ 2x − x = 4 5 3 15

 ⇒ 6x − 5x − 4 15 15

⇒  x = 4 km.
 Here, S1 = 2, 1 t1 = 6 2

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

 = 5 × 3(6 + 10) 2 3 - 5 2

 = 15 × 16 60

 = 16 = 4 km 4

##### Correct Option: A

Let the distance of school be x km.
Difference of time = 6 + 10

 = 16 minutes = 16 hour 60

 = 4 hour 15

 Time = Distance Speed

 ∴ x − x = 4 5/2 3 15

 ⇒ 2x − x = 4 5 3 15

 ⇒ 6x − 5x − 4 15 15

⇒  x = 4 km.
 Here, S1 = 2, 1 t1 = 6 2

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

 = 5 × 3(6 + 10) 2 3 - 5 2

 = 15 × 16 60

 = 16 = 4 km 4

1. A man starts from a place P and reaches the place Q in 7 hours.
 He travels 1 th of the distance at 10 km/hour 4
and the remaining distance at 12 km/hour. The distance between P and Q is
1. 72 km
2. 90 km
3. 80 km
4. 70 km

1.  Time = Distance Speed

According to the question,
 x + 3x = 7 10 12

 ⇒ x + x = 7 10 4

 ⇒ 2x + 5x = 7 20

⇒  7x = 7 × 20
 ∴  x = 7 × 20 = 20 km. 7

∴  PQ = 4x = 4 × 20 = 80 km.

##### Correct Option: C

 Time = Distance Speed

According to the question,
 x + 3x = 7 10 12

 ⇒ x + x = 7 10 4

 ⇒ 2x + 5x = 7 20

⇒  7x = 7 × 20
 ∴  x = 7 × 20 = 20 km. 7

∴  PQ = 4x = 4 × 20 = 80 km.

1. A student starting from his house walks at a
 speed of 2 1 km/hour and reaches his 2
school 6 minutes late. Next day starting at
the same time he increases his speed by 1 km/hour and reaches 6 minutes early. The distance between the school and his house is
1. 4 km
2.  3 1 km 2
3.  1 3 km 4
4. 6 km

1. Distance between school and house = x km (let)

 Time = Distance Speed

According to the question,
 x − x = 6 + 6 = 1 5/2 7/2 60 5

(Difference of time = 6 + 6 =12 minutes)
 ⇒ 2x − 2x = 1 5 7 5

 ⇒ 14x − 10x = 1 ⇒ 4x = 1 35 5 35 5

 ⇒ 4x = 35 = 7 5

 ⇒  x = 7 = 1 3 km. 4 4

Second Method :
 Here, S1 = 2 1 , t1 = 6 2

 S2 = 3 1 , t2 = 6 2

 Distance = (S1 × S2)(t1 + t2) S2 − S1

 = 5 × 7 (6 + 6) 2 2 7 - 5 2 2

 = 35 × 12 4 60

 = 7 = 1 3 km 4 4

##### Correct Option: C

Distance between school and house = x km (let)

 Time = Distance Speed

According to the question,
 x − x = 6 + 6 = 1 5/2 7/2 60 5

(Difference of time = 6 + 6 =12 minutes)
 ⇒ 2x − 2x = 1 5 7 5

 ⇒ 14x − 10x = 1 ⇒ 4x = 1 35 5 35 5

 ⇒ 4x = 35 = 7 5

 ⇒  x = 7 = 1 3 km. 4 4

Second Method :
 Here, S1 = 2 1 , t1 = 6 2

 S2 = 3 1 , t2 = 6 2

 Distance = (S1 × S2)(t1 + t2) S2 − S1

 = 5 × 7 (6 + 6) 2 2 7 - 5 2 2

 = 35 × 12 4 60

 = 7 = 1 3 km 4 4