## Speed, Time and Distance

#### Speed, Time and Distance

1. A bus moving at 40 km per hour covers a distance in 6 hours 15 minutes. If it travels the same distance at 50 km per hour how long will it take to cover the distance ?
1. 2 hrs.
2. 6 hrs.
3. 4 hrs.
4. 5 hrs.

1. Distance = Speed × TIme

 = 40 × 6 1 km 4

 = 40 × 25 km = 250 km 4

New speed = 50 kmph
∴  Required time
 = Distance = 250 = 5 hours Speed 50

Second Method :
 Here, S1 = 40, t1 = 6 15 = 25 60 4

S2 = 50, t2 = ?
S1t1 = S2t2
 40 × 25 = 50 × t2 4

t2 = 5 hrs.

##### Correct Option: D

Distance = Speed × TIme

 = 40 × 6 1 km 4

 = 40 × 25 km = 250 km 4

New speed = 50 kmph
∴  Required time
 = Distance = 250 = 5 hours Speed 50

Second Method :
 Here, S1 = 40, t1 = 6 15 = 25 60 4

S2 = 50, t2 = ?
S1t1 = S2t2
 40 × 25 = 50 × t2 4

t2 = 5 hrs.

1. A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot at the rate 4 kmph and partly on bicycle at the rate 9 kmph. The distance travelled on foot is
1. 16 km
2. 14 km
3. 17 km
4. 15 km

1. Distance travelled by farmer on foot = x km (let)
∴  Distance covered by cycling = (61–x ) km.

 Time = Distance Speed

According to the question,
 x + 61 − x = 9 4 9

 ⇒ 9x + 61 × 4 − 4x = 9 9 × 4

⇒  5x + 244 = 9 × 9 × 4 = 324
⇒  5x = 324 – 244 = 80
 ⇒  x = 80 = 16 km. 5

Second Method :
Here, t = 9, x= 61
u = 4, v = 9
 Time taken = vt − x v − u

 = 9 × 9 − 61 9 − 4

 = 20 = 4 hrs. 5

Distance travelled
= 4 × 4 = 16 km

##### Correct Option: A

Distance travelled by farmer on foot = x km (let)
∴  Distance covered by cycling = (61–x ) km.

 Time = Distance Speed

According to the question,
 x + 61 − x = 9 4 9

 ⇒ 9x + 61 × 4 − 4x = 9 9 × 4

⇒  5x + 244 = 9 × 9 × 4 = 324
⇒  5x = 324 – 244 = 80
 ⇒  x = 80 = 16 km. 5

Second Method :
Here, t = 9, x= 61
u = 4, v = 9
 Time taken = vt − x v − u

 = 9 × 9 − 61 9 − 4

 = 20 = 4 hrs. 5

Distance travelled
= 4 × 4 = 16 km

1. The distance between 2 places R and S is 42 km. Anita starts from R with a uniform speed of 4 km/h towards S and at the same time Romita starts from S towards R also with some uniform speed. They meet each other after 6 hours. The speed of Romita is
1. 18 km/hour
2. 6 km/hour
3. 20 km/hour
4. 8 km/hour
5. None of these

1. Speed of Romita = x kmph
(let)
Distance = Speed × Time
According to the question,
4 × 6 + x × 6 = 42
⇒  6x = 42 – 24 = 18
⇒  x = 18 ÷ 6 = 3 kmph
Second Method :
Distance from R to S = S1t1+S2t2
42 = 4 × 6 + x × 6
6x = 18 x = 3 km/hr.

##### Correct Option: E

Speed of Romita = x kmph
(let)
Distance = Speed × Time
According to the question,
4 × 6 + x × 6 = 42
⇒  6x = 42 – 24 = 18
⇒  x = 18 ÷ 6 = 3 kmph
Second Method :
Distance from R to S = S1t1+S2t2
42 = 4 × 6 + x × 6
6x = 18 x = 3 km/hr.

1. A journey takes 4 hours 30 minutes at a speed of 60 km/hr. If the speed is 15 m/s, then the
journey will take
1. 5 hours
2. 5 hours 30 minutes
3. 6 hours
4. 6 hours 15 minutes

1.  60 kmph = 60 × 5 m/sec 18

 = 50 m/sec. 3

 ∴  Speed ∝ 1 Time

⇒  S1 × T1 = S2 × T2
 ⇒ 50 × 9 = 15 × T2 3 2

 ⇒  T2 = 75 = 5 hours 15

Second Method :
 Here, S1 = 60, t1 = 4 1 = 9 2 2

 S2 = 15 × 18 = 54 5

S1t1 = S2t2
 60 × 9 = 54 × t2 2

 t2 = 270 = 5 hours 54

##### Correct Option: A

 60 kmph = 60 × 5 m/sec 18

 = 50 m/sec. 3

 ∴  Speed ∝ 1 Time

⇒  S1 × T1 = S2 × T2
 ⇒ 50 × 9 = 15 × T2 3 2

 ⇒  T2 = 75 = 5 hours 15

Second Method :
 Here, S1 = 60, t1 = 4 1 = 9 2 2

 S2 = 15 × 18 = 54 5

S1t1 = S2t2
 60 × 9 = 54 × t2 2

 t2 = 270 = 5 hours 54

1. Sriya with her family travelled from Bolpur to Suri by car at a speed of 40 km/hr and returned to Bolpur at a speed of 50 km/hr. The average speed for the whole journey is
1.  44 4 km/hr 9
2. 45 km/hr
3.  45 1 km/hr 2
4. 44.78 km/hr

1.  Average speed of journey = 2xy kmph x + y

 ⇒ 2 × 40 × 50 = 2 × 40 × 50 40 + 50 90

 ⇒ 400 = 44 4 kmph 9 9

##### Correct Option: A

 Average speed of journey = 2xy kmph x + y

 ⇒ 2 × 40 × 50 = 2 × 40 × 50 40 + 50 90

 ⇒ 400 = 44 4 kmph 9 9