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Speed Time & Distance Test 499
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Speed Time & Distance Test 499

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  • Question 1/10
    1 / -0.25
    Sudhin cycled at 8.5 km/h for 4 hours, then took an auto and travelled at 20 km/h for 1.5 hours, and then walked at 4 km/h for y hours. If Sudhin's overall average speed for the entire journey was 10 km/h, what is the value of y?
    Solutions
    Distance travelled at 8.5 km/h = 8.5 × 4 = 34 km

    Distance travelled at 20 km/h = 20×1.5 = 30 km

    Distance travelled at 4 km/h = 4×y = 4y km

    We know that,

    Average speed = Total distance/Total time

    ∴ 10 = [34 + 30 + 4y]/[4 + 1.5 + y]

    ⇒10 = [64 + 4y]/[5.5 + y]

    ⇒ 10[5.5 + y] = [64 + 4y]

    ⇒55 + 10y = 64 + 4y

    ⇒6y = 9

    ⇒ y = 9/6 = 1.5

    Hence, option C is the correct answer.

  • Question 2/10
    1 / -0.25
    A train traveling at 70 km/h crosses another train traveling in the same direction at 34 km/h in 25 seconds. What is the combined length of both the trains (in metres)?
    Solutions
     Given,

    Speed of first train = 70 km/h

    Speed of another train = 34 km/h

    Time to cross = 25 seconds

    Relative speed = 70 – 34 = 36 km/h × 5/18 = 10 m/s (running in same direction)

    Distance travelled = Length of both trains = 25 × 10 = 250 metres

    Hence, option B is the correct answer.

  • Question 3/10
    1 / -0.25
    As part of his journey, a person travels 120 km at 80 km/h, the next 100 km at 40 km/h, and comes back to the starting point at 75 km/h. The average speed of the person throughout the journey (approximately) is:
    Solutions
    Time taken to travel 120 km at 80 km/h

    = 120/80 = 1.5 hr

    Time taken to travel 100 km at 40 km/h

    = 100/40 = 2.5 hr

    Average speed of 220 km distance = Total distance/Total time

    = 220/[1.5 + 2.5] = 55 km/hr

    He comes back to the starting point at the speed of 75 km/hr.

    ∴ Average speed of whole journey = [2 × 55 × 75]/[55 + 75]

    = 63.46 km/h

    Hence, option A is the correct answer.

  • Question 4/10
    1 / -0.25
    Two runners, Sony and Mony, start running on a circular track of length 200 m at speeds of 18 and 24 km/h, respectively, in the same direction. After how much time from the start will they meet again at the starting point?
    Solutions
    Sony and Mony, start running on a circular track of length 200 m at speeds of 18 and 24 km/h, respectively, in the same direction.

    ∴ Relative speed = 24 – 18 = 6 km/hr

    = 6 × 5/18 = 5/3 m/s

    Required time = 200/(5/3)

    = 120 sec

    Hence, option A is the correct answer.

  • Question 5/10
    1 / -0.25
    An athlete crosses a distance of 4800 m in 18 minutes. What is his speed (in km/h)?

    Solutions

    Given, Distance = 4800 m = 4.8 km

    Time = 18 minutes = hrs

    Speed =  = 16 km/h

    Hence, Option C is the correct answer.

  • Question 6/10
    1 / -0.25
    A man makes four trips of equal distances. His speed on first trip was 720 km/hr and in each subsequent trip his speed was half of the previous trip. What is the average speed of the man in these four trips?
    Solutions
     According to the question:

    S1 = 720 km/hr

    S2 = 720/2 = 360 km/hr

    S3 = 360/2 = 180 km/hr

    S4 = 180/2 = 90 km/hr

    Let the distance of each trip be d km.

    ∴ Total distance = 4d

    Average speed = Total distance/Total time

    = 4d/[d/720 + d/360 + d/180 + d/90]

    = 4d/d[(1 + 2 + 4 + 8)/720]

    = 4/[(15)/720]

    = (4)(720)/15

    = 192 km/h

    Hence, option C is the correct answer.

  • Question 7/10
    1 / -0.25
    Ram needs to reach the examination centre in 6 hours, the journey itself is 250 km. If Ram has covered (3/5)th of the distance in 3.5 hours then what is the speed required to reach the destination 30 minutes early than the required time?
    Solutions

    Actual time to reach examination centre = 6 – 0.5 = 5.5 hours

    3/5 of total distance = (3/5) × 250 = 150 km

    Remaining distance = 250 – 150 = 100 km

    Remaining time = 5.5 – 3.5 = 2 hours

    Speed = Distance/time

    = 100/2 = 50 km/h

    Hence, option A is the correct answer.

  • Question 8/10
    1 / -0.25
    Two trains with a speed of 80 km/h and 120 km/h, respectively, are 500 km apart and face each other. Find the distance between them 10 minutes before crossing.

    Solutions

    Speed of first train = 80 km/h

    Speed of second train = 120 km/h

    Relative speed = 120 + 80 = 200 km/h

    Distance between them 10 minutes before crossing = Speed × Time

    = 200 ×  =  = 33.33 km

    Hence, option B is the correct answer.

  • Question 9/10
    1 / -0.25
    Two trains, running between Bangalore and Chennai, start at the same time from their respective locations and proceed towards each other at the speed of 80km/h and 95km/h. When they meet, it is found that one train has travelled 180km more than the other.The distance between Bangalore and Chennai is _______.

    Solutions

    In one hour faster train travel 95 – 80 = 15 km more distance.

    Time taken by 180 km more distance =  = 12 hours

    Relative speed = 80 + 95 = 175 km/h

    Distance between Bangalore and Chennai = 175 × 12 = 2100 km

    Hence, option B is the correct answer.

  • Question 10/10
    1 / -0.25
    A car travels with a speed of 21 m/sec in the first 10 minutes, 9.0 km in the next 10 minutes and 10 km in the last 10 minutes of its journey. What is the average speed of the car in km/h during its entire journey?

    Solutions

    Speed = 21 m/s =  

    In first 10 minutes distance travelled by car =  = 12.6 km

    Total distance = 12.6 + 9 + 10 = 31.6 km

    Total time = 10 + 10 + 10 = 30 minutes =  hours = 0.5 hours

     Average speed =

    =  = 63.2 km/h

    Hence, option B is the correct answer.

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