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. View Hint View Answer Discuss in Forum

    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
    49

    ⇒ 
    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
    49

    ⇒ 
    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. View Hint View Answer Discuss in Forum

    ∵  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. View Hint View Answer Discuss in Forum

    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. View Hint View Answer Discuss in Forum

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

    1200
    1200
    = 2
    x − 300x

    ⇒  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 − 300x

    ⇒  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. View Hint View Answer Discuss in Forum

    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