Speed, Time and Distance

Speed, Time and Distance

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  1. The speed of a motorboat is 30 km/h. It starts from Mumbai at 6 am and reaches Goa at 8 am. Same day, it starts from Goa at 12 pm and reaches Mumbai at 4 pm. Find the the speed of stream.








  1. View Hint View Answer Discuss in Forum

    Clearly, motorboat takes 2 h go from Mumbai to Goa and 4 h to go from Goa to Mumbai. i.e.,
    Time taken to row upstream = 2 x Time taken to row downstream
    ∴ n = 2
    Let the speed of stream be V km/h.
    According to the formula,
    Speed of boat = V(n + 1)/(n - 1)

    Correct Option: C

    Clearly, motorboat takes 2 h go from Mumbai to Goa and 4 h to go from Goa to Mumbai. i.e.,
    Time taken to row upstream = 2 x Time taken to row downstream
    ∴ n = 2
    Let the speed of stream be V km/h.
    According to the formula,
    Speed of boat = V(n + 1)/(n - 1)
    ⇒ 30 = V(2 + 1)/(2 - 1)
    ∴ V = 30/3 = 10 km/h

  1. The current of a stream runs at 1 km/h. A motorboat goes 35 km upstream and back again at the starting point in 12 h. What is the speed of motorboat in still water ?








  1. View Hint View Answer Discuss in Forum

    Let the speed of boat in still water be V km/h. Then,
    35/(V - 1) + 35/(V + 1) = 12
    ⇒ 35(V + 1 + V - 1) = 12(V2 - 1)

    Correct Option: C

    Let the speed of boat in still water be V km/h. Then,
    35/(V - 1) + 35/(V + 1) = 12
    ⇒ 35(V + 1 + V - 1) = 12(V2 - 1)
    ⇒ 6V2 - 35V - 6 = 0
    ⇒ (V - 6)(6V + 1) = 0
    ⇒ V = 6 (V = - 1/6 is not possible)
    So, speed of boat in still water is 6 km/h.

  1. A streamer goes downstream from one port to another in 4 h. It covers the same distance upstream in 5 h. If the speed of the stream is 2 km/h , find the distance between the two ports ?








  1. View Hint View Answer Discuss in Forum

    Let the distance between the two ports = L km
    Then, speed downstream = L/4
    and speed upstream = L/5
    ∴ Speed of the stream = 1/2(L/4 - L/5)

    Correct Option: D

    Let the distance between the two ports = L km
    Then, speed downstream = L/4
    and speed upstream = L/5
    ∴ Speed of the stream = 1/2(L/4 - L/5)
    ⇒ 1/2[(5L - 4L)/20] = 2
    ⇒ L = 80 km

  1. A person can row 71/2 km/h in still water. It takes him twice as long to row up a distance as to row down the same distance. Find the speed of the stream ?








  1. View Hint View Answer Discuss in Forum

    Speed upstream + Speed downstream = 2 x 71/2 = 15 km/h
    Since, the time taken is in the ratio 2 : 1
    hence the speed will be in the ratio 1 : 2
    ∴ Speed upstream = (1/3) x 15 = 5 km/h
    and speed downstream = (2/3) x 15 = 10 km/h

    Correct Option: C

    Speed upstream + Speed downstream = 2 x 71/2 = 15 km/h
    Since, the time taken is in the ratio 2 : 1
    hence the speed will be in the ratio 1 : 2
    ∴ Speed upstream = (1/3) x 15 = 5 km/h
    and speed downstream = (2/3) x 15 = 10 km/h
    ∴ Speed of stream = (10 - 5)/2 = 2.5 km/h

  1. A thief running at 8 km/h is chased by a policeman whose speed is 10 km/h. If the thief is 100 m ahead of the policeman, then the time required for the policeman to catch the thief will be








  1. View Hint View Answer Discuss in Forum

    Relative speed of policeman with thief = (10 - 8) = 2 km/h
    Now, time taken to cover 100 m with speed of 2 km/h or 2000 m/h

    Now, Speed = Distance / Time
    ∴ Time = D/S = 100/2000

    Correct Option: B

    Relative speed of policeman with thief = (10 - 8) = 2 km/h
    Now, time taken to cover 100 m with speed of 2 km/h or 2000 m/h

    Now, Speed = Distance / Time
    ∴ Time = D/S = 100/2000
    = 1/20 h or 60/20 min = 3 min