## Speed, Time and Distance

#### Speed, Time and Distance

1. A train starts from A at 7 a.m. towards B with speed 50 km/h. Another train starts from B at 8 a.m. with speed 60 km/h towards A. Both of them meet at 10 a.m. at C. The ratio of the distance AC to BC is
1. 5 : 6
2. 5 : 4
3. 6 : 5
4. 4 : 5

1. AC = Distance covered by train starting from A in 3 hours
= 50 × 3 = 150 km
BC = Distance covered by train starting from B in 2 hours
= 60 ×2 = 120 km
∴  AC : BC = 150 : 120 = 5 : 4

##### Correct Option: B AC = Distance covered by train starting from A in 3 hours
= 50 × 3 = 150 km
BC = Distance covered by train starting from B in 2 hours
= 60 ×2 = 120 km
∴  AC : BC = 150 : 120 = 5 : 4

1. The ratio of length of two trains is 5 : 3 and the ratio of their speed is 6 : 5. The ratio of time
taken by them to cross a pole is
1. 5 : 6
2. 11 : 8
3. 25 : 18
4. 27 : 16

1. Required ratio

 = 5 : 3 = 30 × 5 : 30 × 3 6 5 6 5

= 25 : 18

##### Correct Option: C

Required ratio

 = 5 : 3 = 30 × 5 : 30 × 3 6 5 6 5

= 25 : 18

1. The speed of A and B are in the ratio 3 : 4. A takes 20 minutes more than B to reach a destination. In what time does A reach the destination ?
1.  1 1 hours 3
2. 2 hours
3.  2 2 hours 3
4.  1 2 hours 3

1. Ratio of speed = 3 : 4
Ratio of time taken = 4 : 3
Let the time taken by A and B be 4x hours and 3 x hours respectively.

 Then, 4x–3x = 20 ⇒ x = 1 60 3

∴  Time taken by A = 4x hours
 = 4 × 1 hours 3

 = 1 1 hours 3

Second Method :
Here, S1 = 3x, S2 = 4x
 t2= y, t1 = y + 20 = y + 1 60 3

S1t1 = S2t2
 3x y + 1 = 4xy 3

 ∴  Time taken by A = 1 + 1 = 1 1 hours 3 3

##### Correct Option: A

Ratio of speed = 3 : 4
Ratio of time taken = 4 : 3
Let the time taken by A and B be 4x hours and 3 x hours respectively.

 Then, 4x–3x = 20 ⇒ x = 1 60 3

∴  Time taken by A = 4x hours
 = 4 × 1 hours 3

 = 1 1 hours 3

Second Method :
Here, S1 = 3x, S2 = 4x
 t2= y, t1 = y + 20 = y + 1 60 3

S1t1 = S2t2
 3x y + 1 = 4xy 3

 ∴  Time taken by A = 1 + 1 = 1 1 hours 3 3

1. In covering a certain distance, the speed of A and B are in the ratio of 3 : 4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is :
1. 1 hour
2.  1 1 hours 2
3. 2 hours
4.  2 1 hours 2

1. Let the distance of destination be D km
Let the speed of A = 3x km/hr
then speed of B = 4x km/hr
∴  According to question,

 D − D = 30 minutes 3x 4x

 = 1 hr 2

 ∴ D = 1 12x 2

 ⇒ D = 4 = 2 hours 3x 2

Hence, time taken by A to reach
destination = 2hrs.

Second Method :
Here, S1 = 3x, S2 = 4x
 t2= y, t1 = y + 30 = y + 1 60 2

S1t1 = S2t2
 3x × y + 1 = 4 x × y 2

 3y + 3 = 4y 2

 y = 3 2

 ∴  Time taken by A = 3 + 1 = 2 hrs. 2 2

##### Correct Option: C

Let the distance of destination be D km
Let the speed of A = 3x km/hr
then speed of B = 4x km/hr
∴  According to question,

 D − D = 30 minutes 3x 4x

 = 1 hr 2

 ∴ D = 1 12x 2

 ⇒ D = 4 = 2 hours 3x 2

Hence, time taken by A to reach
destination = 2hrs.

Second Method :
Here, S1 = 3x, S2 = 4x
 t2= y, t1 = y + 30 = y + 1 60 2

S1t1 = S2t2
 3x × y + 1 = 4 x × y 2

 3y + 3 = 4y 2

 y = 3 2

 ∴  Time taken by A = 3 + 1 = 2 hrs. 2 2

1. In covering a certain distance, the speed of A and B are in the ratio of 3 : 4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is :
1. 1 hour
2.  1 1 hours 2
3. 2 hours
4.  2 1 hours 2

1. Let the distance of destination be D km
Let the speed of A = 3x km/hr
then speed of B = 4x km/hr
∴  According to question,

 D − D = 30 minutes 3x 4x

 = 1 hr 2

 ∴ D = 1 12x 2

 ⇒ D = 4 = 2 hours 3x 2

Hence, time taken by A to reach
destination = 2hrs.

Second Method :
Here, S1 = 3x, S2 = 4x
 t2= y, t1 = y + 30 = y + 1 60 2

S1t1 = S2t2
 3x × y + 1 = 4 x × y 2

 3y + 3 = 4y 2

 y = 3 2

 ∴  Time taken by A = 3 + 1 = 2 hrs. 2 2

##### Correct Option: C

Let the distance of destination be D km
Let the speed of A = 3x km/hr
then speed of B = 4x km/hr
∴  According to question,

 D − D = 30 minutes 3x 4x

 = 1 hr 2

 ∴ D = 1 12x 2

 ⇒ D = 4 = 2 hours 3x 2

Hence, time taken by A to reach
destination = 2hrs.

Second Method :
Here, S1 = 3x, S2 = 4x
 t2= y, t1 = y + 30 = y + 1 60 2

S1t1 = S2t2
 3x × y + 1 = 4 x × y 2

 3y + 3 = 4y 2

 y = 3 2

 ∴  Time taken by A = 3 + 1 = 2 hrs. 2 2