Speed, Time and Distance

Speed, Time and Distance

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  1. Two ladies simultaneousely leave cities A and B connected by a strainght road and travel towards each other. The first lady travels 2km/h faster than the second lady and reaches B one hour before the second lady reaches A. The two cities A and B are 24 km apart. How many kilometres does each lady travel in one hour ?








  1. View Hint View Answer Discuss in Forum

    Let the speed of first lady be (v + 2)km/h and speed of second lady will be v km/h.
    Total distance = 24 km

    For first lady, Speed = Distance/Time
    v + 2 = 24/t ...(i)

    Let time taken by first lady to cover distance of 24 km be t h.
    Then, time taken by second lady to cover same distance will be(t + 1)h.
    For second lady, Speed =Distance/time
    v = 24/(t + 1) ...(ii)

    Correct Option: C

    Let the speed of first lady be (v + 2)km/h and speed of second lady will be v km/h.
    Total distance = 24 km

    For first lady, Speed = Distance/Time
    v + 2 = 24/t ...(i)

    Let time taken by first lady to cover distance of 24 km be t h.
    Then, time taken by second lady to cover same distance will be(t + 1)h.
    For second lady, Speed =Distance/time
    v = 24/(t + 1) ...(ii)

    Form Eqs.(i) and (ii), we get
    24/t - 2 = 24/(t + 1)
    ⇒ (24 - 2t)/t = 24/(t + 1)
    ⇒ (24 - 2t)(t + 1) = 24t
    ⇒ 24t - 2t2 + 24 - 2t = 24t
    ⇒ 2t2 + 2t - 24 = 0
    ⇒ t2 + t - 12 = 0
    ⇒ t2 + 4t - 3t - 12 = 0
    ⇒ t(t + 4) -3(t + 4) = 0
    ⇒ (t - 3)(t + 4) = 0
    ⇒ t = 3, -4
    ∴ t = 3 (t ≠- 4)
    ∴ The distance travelled by the first lady in one hour
    = 24/t = 24/3 = 8 km
    And distance travelled by the second lady in one hour
    = 24/t + 1
    = 24/3 + 1 = 6 km

  1. A thief sees a jeep at a distance of 250 m, coming towards him at 36 km/h. Thief takes 5 seconds to realise that there is nothing but the police is approaching him by the jeep and start running away from police at 54 km/h. But police realise after 10 seconds, when the thief starts running away, that he is actually a thief and gives chase at 72 km/h. how long after thief saw police did police catchup with him and what is the distance police had to travel to do so ?








  1. View Hint View Answer Discuss in Forum

    Initial speed of police = 10 m/s
    Increased speed of police = 20 m/s
    Speed of thief = 15 m/s
    Initial difference between thief and police = 250 m
    After 5 seconds difference between thief and police = 250 - (5 x 10) = 200 m
    After 10 seconds more, the difference between thief and police = 200 + (5 x 10) = 250 m.
    Now, the time required by police to catch the thief = 250/5 = 50 sec.

    Correct Option: B

    Initial speed of police = 10 m/s
    Increased speed of police = 20 m/s
    Speed of thief = 15 m/s
    Initial difference between thief and police = 250 m
    After 5 seconds difference between thief and police = 250 - (5 x 10) = 200 m
    After 10 seconds more, the difference between thief and police = 200 + (5 x 10) = 250 m.
    Now, the time required by police to catch the thief = 250/5 = 50 s
    Distance travelled = 50 x 20 = 1000 m
    Total time = 50 + 15 = 65 sec
    Total distance = 1000 + (15 x 10) = 1150 m

  1. Suresh traveled 1200 km by air which formed (2/5) of his trip. One-third of the whole trip he traveled by car And the rest of the journey he performed by train. The distance traveled by train was ?








  1. View Hint View Answer Discuss in Forum

    Let the total distance be y km.
    Then, 2y / 5 = 1200
    ⇒ y = (1200 x 5) /2 = 3000 km.

    Distance traveled by car
    = (1/3 X 3000) = 1000 km.

    Correct Option: B

    Let the total distance be y km.
    Then, 2y / 5 = 1200
    ⇒ y = (1200 x 5) /2 = 3000 km.

    Distance traveled by car
    = (1/3 X 3000) = 1000 km.

    Distance traveled by train
    = [3000- (1200 + 1000) ] km.
    = 800 km.

  1. Two cyclists A and B start from the same place at the same time. One going toward north at 18 km/hr. and other going toward south at 20 km/hr. What time will they take to be 95 km. apart ?








  1. View Hint View Answer Discuss in Forum

    Relative velocity = u + v = 18 + 20 = 38 km
    They are 38 km. apart in 1 hr.

    Correct Option: D

    Relative velocity = u + v = 18 + 20 = 38 km
    They are 38 km. apart in 1 hr.
    ∴ They will be 95 km. apart in ( 95 / 38) hrs.
    = 2 hrs . 30 min

  1. A bullock cart has to cover a distance of 80 km. in 10 hours. If it cover half of journey in 3/5th time, what should be its speed to cover the remaining distance in time left ?








  1. View Hint View Answer Discuss in Forum

    Distance left = (1/2 x 80 ) km. = 40km.
    Time left - [(1-3/5) x 10 ] hrs.
    = 4 hours

    Correct Option: D

    Distance left = (1/2 x 80 ) km. = 40km.
    Time left - [(1-3/5) x 10 ] hrs.
    = 4 hours

    Required speed = (40 / 4 ) km/hr
    = 10 km/hr.