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27 June, 21:00

In the Netherlands, there is an annual ice-skating race called the "Tour of the Eleven Towns." The total distar. rce of the course is 2.00 x 102 krn, and the record time for covering it is 5 h, 40 min, 37 s. a. Calculate the average speed of the record race. b. If the first half of the distance is covered by a skater moving with a speed o[ 1.05v, where y is the average speed found in (a), how long will it take to skate the first halft Express your answer in hours and minutes.

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  1. 27 June, 22:53
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    a) The average speed of the record race is 35.2 km/h

    b) The time it will take to cover the first half is 2h 42 min

    Explanation:

    a) The average speed of the record race is calculated dividing the total distance over time:

    v = distance / time

    So let's write the time in hours:

    if 60 s is 1 min, then 37 s will be (37 s · 1 min/60 s) 0.62 min.

    If 60 min is 1 h, then 40.62 min will be (40.62 min · 1 h/60 min) 0.68 h

    Then, the record time is 5.68 h

    The average speed will be:

    v = 2.00 * 10² km / 5.68 h = 35.2 km/h

    b) Now we have the speed and the distance and have to find the time it will take the skater to cover that distance:

    The speed will be:

    v = 1.05v = 1.05 · 35.2 km/h = 37.0 km/h

    The distance will be:

    2.00 * 10² km / 2 = 1.00 * 10² km

    Then:

    v = distance / time

    time = distance / v = 1.00 * 10² km / 37.0 km/h = 2.70 h

    If 1 h is 60 min, 0.70 h will be (0.70 h · 60 min/h) 42 min.

    The time it will take to cover the first half is 2h 42 min
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