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.

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