Speed, Time and Distance


  1. A student goes to his school from his house walking at 4 km/h and reaches his school 10 min late. Next day, starting at the same time he walks as 6 km/h and reaches his school 5 min earlier than the scheduled time. Find the distance between school and home ?









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    Let the distance be x km.
    ∴ Time = Distance/speed
    1st day time taken = x/4 h
    2nd day time taken = x/6 h
    Difference in time = (x/4 - x/6) h
    Actual difference between these two times = 15 min = 1/4 h
    ∴ x/4 - x/6 = 1/4 ⇒ (3x - 2x)/12 = 1/4

    Correct Option: B

    Let the distance be x km.
    ∴ Time = Distance/speed
    1st day time taken = x/4 h
    2nd day time taken = x/6 h
    Difference in time = (x/4 - x/6) h
    Actual difference between these two times = 15 min = 1/4 h
    ∴ x/4 - x/6 = 1/4 ⇒ (3x - 2x)/12 = 1/4
    ∴ x = 3 km


  1. Two train of length 250 m and 140 m are running on parallel lines in the same direction at 58 km/h and 32 km/h, respectively. Find the time taken by the slower train to pass the driver of the faster one ?









  1. View Hint View Answer Discuss in Forum

    Relative speed = (58 - 32) = 26 km/h
    = 26 x (5/18) m/s = 65/9 m/s
    Time taken to cross each other = (250 + 140)/(65/9)

    Correct Option: B

    Relative speed = (58 - 32) = 26 km/h
    = (26 x 5/18) m/s = 65/9 m/s
    Time taken to cross each other = (250 + 140)/(65/9)
    = (390 x 9)/65 = 54 s



  1. A person travelled a distance of 50 km in 8 h. He covered a part of the distance on foot at the rate of 4 km/h and a part on a bicycle at the rate of 10 km/h. How much distance did he travel on foot ?









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    Let T h, he travels on foot.
    ∴ 4T + 10(8 - T) = 50

    Correct Option: B

    Let T h, he travels on foot.
    ∴ 4T + 10(8 - T) = 50
    ⇒ 80 - 6T = 50
    ⇒ 6T = 30,
    ∴ T = 5 h
    ∴ The distance travelled on foot = 4 x 5 = 20 km


  1. Total time taken by a person in going to a place by walking and returning on cycle is 5 h 45 min. He would have gained 2 h by cycling both ways. The time taken by him to walk both ways, is ?









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    Walking time + Cycling time = 5 h 45 min = 345 min ....(i)
    If he had cycled both way he would have gained 2 h (120 min).
    ∴ 2 x Cycling time = 345 - 120 = 225 min ...(ii)
    Walking time = 2 x 345 - 225 = 690 - 225 = 465 min

    Correct Option: B

    Walking time + Cycling time = 5 h 45 min = 345 min ....(i)
    If he had cycled both way he would have gained 2 h (120 min).
    ∴ 2 x Cycling time = 345 - 120 = 225 min ...(ii)
    Walking time = 2 x 345 - 225 = 690 - 225 = 465 min
    Time taken by him to walk both ways = 7 h 45 min



  1. Amit start from a point A and walks to another point B and then return from B to A by his car and thus takes a total time of 6 h 45 min. If he had driven both ways in his car, he would have taken 2 h less. How long would it take for him to walk both ways ?









  1. View Hint View Answer Discuss in Forum

    Let w be the time taken in one way by walking and c be the time taken in one way by car.
    Now, according to the question,
    In first case, w + c = 6 h 45 min
    or
    2w + 2c = 13 h 30 min ..(i)
    In second case, 2c = 4 h 45 min ....(ii)
    From Eqs. (i) and (ii), we get
    2w + 2c = 13 h 30 min

    Correct Option: D

    Let w be the time taken in one way by walking and c be the time taken in one way by car.
    Now, according to the question,
    In first case, w + c = 6 h 45 min
    or
    2w + 2c = 13 h 30 min ..(i)
    In second case, 2c = 4 h 45 min ....(ii)
    From Eqs. (i) and (ii), we get
    2w + 2c = 13 h 30 min
    ⇒ 2w + 4h 45 min = 13 h 30 min
    ⇒ 2w = 13 h 30 min - 4 h 45 min
    ⇒ 2w = 8 h 45 min
    ∴ If he walks both ways, then time taken = 8 h 45 min