## Speed, Time and Distance

#### Speed, Time and Distance

1. A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot at a speed of 4 km/hour and partly on bicycle at a speed of 9 km/hour. The distance travelled on foot is :
1. 14 km.
2. 16 km.
3. 20 km.
4. 18 km.

1. Length of journey on foot = x km. (let).
∴  Length of journey on cycle = (61 – x ) km.
According to the question,

 Time = Distance Speed

 ∴ x + 61 − x = 9 4 9

 ⇒ 9x + 244 − 4x = 9 36

⇒  5x + 244 = 36 × 9 = 324
⇒  5x = 324 – 244 = 80
 ⇒  x = 80 = 16 km 5

##### Correct Option: B

Length of journey on foot = x km. (let).
∴  Length of journey on cycle = (61 – x ) km.
According to the question,

 Time = Distance Speed

 ∴ x + 61 − x = 9 4 9

 ⇒ 9x + 244 − 4x = 9 36

⇒  5x + 244 = 36 × 9 = 324
⇒  5x = 324 – 244 = 80
 ⇒  x = 80 = 16 km 5

1. Ravi has a roadmap with a scale of 1.5 cm for 18 km. He drives on that road for 72 km. What would be his distance covered in that map?
1. 4 cm
2. 6 cm
3. 8 cm
4. 7 cm

1. ∵  18 km ≡ 1.5 cm

 ∴  1 km ≡ 1.5 cm 18

##### Correct Option: B

∵  18 km ≡ 1.5 cm

 ∴  1 km ≡ 1.5 cm 18

1. A motor cycle gives an average of 45 km per litre. If the cost of petrol is Rs. 20 per litre, the amount required to complete a journey of 540 km is, (in Rupees)
1. 120
2. 360
3. 200
4. 240

1. Consumption of petrol in covering 540 km

 = 540 = 12 litres 45

∴  Required expenses
= Rs. (12 × 20)
= Rs. 240

##### Correct Option: D

Consumption of petrol in covering 540 km

 = 540 = 12 litres 45

∴  Required expenses
= Rs. (12 × 20)
= Rs. 240

1. Due to inclement weather, an air plane reduced its speed by 300 km/hr, and reached the destination of 1200 km late by 2hrs. Then the schedule duration of the flight was
1. 1 hour
2. 1.5 hours
3. 2 hours
4. 2.5 hours

1. Let the original speed of aeroplane be x kmph.
According to the question,

 1200 − 1200 = 2 x − 300 x

 ⇒  1200 x − x + 300 = 2 x(x − 300)

 ⇒  x (x – 300) = 1200 × 300 2

⇒  x (x – 300) = 600 × 300
⇒  x (x – 300) = 600 (600 – 300)
⇒  x = 600 kmph.
 ∴  Scheduled duration of flight = 1200 = 2 hours 600

##### Correct Option: C

Let the original speed of aeroplane be x kmph.
According to the question,

 1200 − 1200 = 2 x − 300 x

 ⇒  1200 x − x + 300 = 2 x(x − 300)

 ⇒  x (x – 300) = 1200 × 300 2

⇒  x (x – 300) = 600 × 300
⇒  x (x – 300) = 600 (600 – 300)
⇒  x = 600 kmph.
 ∴  Scheduled duration of flight = 1200 = 2 hours 600

1. A man can cover a certain distance in 3 hours 36 minutes if he walks at the rate of 5 km/hr. If he covers the same distance on cycle at the rate of 24 km/hr, then the time taken by him in minutes is
1. 40
2. 45
3. 50
4. 55

1. Distance covered in 3 hours 36 minutes

 i.e.   3 36 hours 60

 i.e.   3 3 hours 5

 = 5 × 18 = 18 km. 5

∴  Time taken at 24 kmph.
 = 18 hour 24

 = 18 × 60 minutes 24

= 45 minutes

##### Correct Option: B

Distance covered in 3 hours 36 minutes

 i.e.   3 36 hours 60

 i.e.   3 3 hours 5

 = 5 × 18 = 18 km. 5

∴  Time taken at 24 kmph.
 = 18 hour 24

 = 18 × 60 minutes 24

= 45 minutes