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Speed, Time And Distance Test - 1

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Speed, Time And Distance Test - 1
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  • Question 1
    3 / -1

    A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?

    Solution

    To find the person's speed in km per hour, we first need to convert the distance they traveled and the time they took to cover that distance to the appropriate units. Since there are 60 minutes in an hour, the person's journey took 5 / 60 = 0.0833 hours. The distance they traveled in km is 600 m / 1000 m/km = 0.6 km.

    The person's speed is then given by the distance they traveled divided by the time they took to cover that distance. Therefore, the person's speed is 0.6 km / 0.0833 hours = 7.2 km/hr.

    Therefore, the person's speed is 7.2 km/hr. The correct answer is 7.2 km/hr.

  • Question 2
    3 / -1

     

    A man takes 5 hours 45 min in walking to a certain place and riding back. He would have gained 2 hours by riding both ways. The time he would take to walk both ways, is:

     

    Solution

     

     

    Given that time taken for riding both ways will be 2 hours lesser than the time needed for walking one way and riding back.

    From this, we can understand that
    Time needed for riding one way = time needed for walking one way - 2 hours

    Given that time taken in walking one way and riding back = 5 hours 45 min

    Hence, the time he would take to walk both ways = 5 hours 45 min + 2 hours = 7 hours 45 min

     

     

  • Question 3
    3 / -1

    Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?

    Solution

    Due to stoppages, it covers 9 km less in an hour.

    Time taken to cover 9 km =(9/54 )*60 min = 10 min.

  • Question 4
    3 / -1

    A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.

    Solution

    Let time taken to travel the first half = x hr 
    ⇒ Time taken to travel the second half = (10 - x) hr 

    ∵ Distance = Time * Speed
    Distance covered in the first half = 21x 
    Distance covered in the the second half = 24(10 - x)

    ∵  Distance covered in the the first half = Distance covered in the the second half
    ⇒ 21x = 24(10 - x)
    ⇒ 45x = 240
    ⇒ x = 16/3

    Total Distance = 2 * 21(16/3) = 224 Km [∵ multiplied by 2 as 21x was the distance of half way]

  • Question 5
    3 / -1

    A car traveling with 5/7 of its actual speed covers 42 km in 1 hr 40 min 48 sec. What is the actual speed of the car?

    Solution

    Time taken = 1 hr 40 min 48 sec = 1 hr (40 + 4/5) min = 1 + 51/75 hrs = 126/75 hrs
    Let the actual speed be x km/hr
    Then, (5/7) * x * (126/75) = 42
    ⇒ x = 42 * 7 * (75 / 5) * 126
    ⇒ x = 35 km/hr

  • Question 6
    3 / -1

    A man covered a certain distance at some speed. If he had moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. What is the the distance in km?

    Solution

    According to given condition:

    • vt = (v + 3) (t - 2/3)
    • vt = (v - 2) (t + 2/3)

    On solving we will get:
    t = 10/3 hrs and v = 12 km/hr

    So, distance = (10/3) * 12 = 40 km

  • Question 7
    3 / -1

    A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 9.30 a.m.?

    Solution

    Relative speed = Speed of A + Speed of B = 2 + 3 = 5 rounds per hour
    (∴ they walk in opposite directions)

    ⇒ They cross each other 5 times in 1 hour and 2 times in 1/2 hour

    ∵ Time duration from 8 a.m. to 9.30 a.m. = 1.5 hour

    ∴ They cross each other 7 times before 9.30 a.m

  • Question 8
    3 / -1

    Two boys starts from the same place walking at the rate of 5 kmph and 5.5 kmph respectively in the same direction. What time will they take to be 8.5 km apart?

    Solution

    In this type of question, we need to get the relative speed between them.

    The relative speed of the boys = 5.5 – 5 = 0.5 km/h

    The distance between them is 8.5 km.
    Time = Distance/Speed
    Time = 8.5/0.5 = 17 hrs

  • Question 9
    3 / -1

    In covering a distance of 30 km, Arun takes 2 hours more than Anil. If Arun doubles his speed, then he would take 1 hour less than Anil. What is Arun's speed?

    Solution

    Let Anil takes x hrs.
    ⇒ Arun takes x+2

    If Arun doubles the speed, he will take x-1 hrs
    ⇒ He needs 3 hours less.
    ∵ Double speed means half time.
    ∴ Half of the time required by Arun to cover 30 km = 3 hours

    ⇒ Time required by Arun to cover 30 km = 6 hour
    Thus, Arun's speed = 30/6 = 5 km/h

  • Question 10
    3 / -1

    A car travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. What is the average speed for the first 320 km of the tour?

    Solution

    Total time taken = (160/64) + (160/80) = 9/2 hrs
    ∴ Average speed = 320 x (2/9) = 71.11 km/hr.

  • Question 11
    3 / -1

    A jeep travels a distance of 100 km at a uniform speed. If the speed of the jeep is 5 kmph more, then it takes 1 hour less to cover the same distance. The original speed of the jeep is:

    Solution

    Let the original speed of the jeep be x kmph.

    ⇒100/x−100/(x+5)=1

    Solving this, we get x = 20 kmph.

  • Question 12
    3 / -1

    Two athletes cover the same distance at the rate of 10 and 15 kmph respectively. Find the distance travelled when one takes 15 minutes longer than the other.

    Solution

    Let the distance be D km.

    ⇒ D/10−D/15 = 15/60

    ⇒ D/30 = 1/4

    ⇒ D = 7.5 km

  • Question 13
    3 / -1

    If Sita walks at 5 kmph, she misses her train by 10 minutes. If she walks at 7 kmph, she reaches the station 10 minutes early. How much distance does she walk to the station?

    Solution

    Let the distance be D.

    D/5−D/7=(10+10)/60

    ⇒ D = 35/6 = 5.8km

  • Question 14
    3 / -1

    A friend is spotted by Lalloo at a distance of 200 m. When Lalloo starts to approach him, the friend also starts moving in the same direction as Lalloo. If the speed of his friend is 15 kmph, and that of Lalloo is 20 kmph, then how far will the friend have to walk before Lalloo meets him?

    Solution

    Lalloo is unfortunate that the friend is moving away from him.

    (Because the friend moves in same direction as Lalloo).

    relative speed= 20- 15= 5,kmph. distance= 200 m.

    Thus, Lalloo will meet his friend when he gains 200 m over him.

    => time required = distance / speed = 0.2/5 = 1/25 hrs.

    => Distance travelled by the friend in 1/25 hrs. (when Lalloo catches up him)

    => Time x Speed = 1/25 x 15 = 3/5 km = 600 m

  • Question 15
    3 / -1

    A person going from Pondicherry to Ootacamond travels 120 km by steamer, 450 km by rail and 60 km by horse transit. The journey occupies 13 hours 30 minutes, and the speed of the train is three times that of the horse-transit and 1(1/2) times that of the steamer. Find the speed of the train.

    Solution

    To find the speed of the train, we first need to find the speed of the steamer and the speed of the horse transit. The total distance traveled is 120 km + 450 km + 60 km = 630 km, and the total time taken for the journey is 13.5 hours. Therefore, the average speed of the journey is 630 km / 13.5 hours = 46.67 km/hr.

    Since the speed of the train is three times that of the horse-transit and 1.5 times that of the steamer, we can write the following equations:

    t = 3h t = 1.5s

    where t is the speed of the train, h is the speed of the horse transit, and s is the speed of the steamer. Solving these equations, we find that the speed of the horse transit is 23.01 km/hr and the speed of the train is 69.03 km/hr.

    Therefore, the speed of the train is 69.03 km/hr. The correct answer is B

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