Vivian plays ice hockey and gets to her training sessions by bike. For warm up, she skates the rink from one end to the other and back 5 times, while for cool down, she calmly skates the rink from one end to the other only 3 times. The hockey rink is 56.45 meters long. After her training session she jumps on her bike and heads off home, which is 6.8 kilometers away. Halfway down the road she notices that she left her keys at the arena and rides back to retrieve them. a) How many meters does Vivian skate for warm up? b) How many meters does Vivian skate for cool down? c) How many meters does she skate for warm up and cool down in total? d) How many kilometers extra does Vivian have to ride due to leaving her keys behind? e) Once back at home, how many kilometers did Vivian ride in total?
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Once back at home, Vivian rode a total distance of her regular ride home plus the extra distance she had to ride to retrieve her keys. So, the total distance she rode is 6.8 + 3.4 = 10.2 kilometers.

To determine how many kilometers extra Vivian has to ride due to leaving her keys behind, we need to calculate the distance between the arena and the halfway point on her way home. The total distance from her home to the arena is 6.8 kilometers, so the halfway point is at 6.8 / 2 = 3.4 kilometers. Vivian rides back this distance to retrieve her keys, resulting in an extra ride of 3.4 kilometers.

The total distance Vivian skates for warm up and cool down is the sum of the distances calculated in parts a and b. So, she skates a total distance of 564.5 + 338.7 = 903.2 meters for warm up and cool down.

For cool down, Vivian skates the rink from one end to the other only 3 times. Therefore, she skates a distance of 3 * 2 * 56.45 = 338.7 meters for cool down.

Vivian skates the rink from one end to the other and back 5 times for warm up. The length of the rink is 56.45 meters, so she skates a total distance of 5 * 2 * 56.45 = 564.5 meters for warm up.