10. Dava is training for a sprint triathlon consisting of a 3 mile run, followed by...

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10. Dava is training for a sprint triathlon consisting of a 3 mile run, followed by a 20 mile bike ride, and ending with a half mile swim. Recently, she has completed three training sessions with total times shown in the table below. 3.5 run (mi) bike (mi) swim (mi) time (min) 2 ½/₂ 35 10 1 60 0 1 65 Coordinate Spaces 205 4 Calculate Dava's expected triathlon time using two different methods. (a) Compute the rates at which Dava can expect to perform in each event (minutes per mile) assuming that all times scale linearly with distance. Then determine her total expected time. (b) Consider Dava's training run distances as vectors in R³. Show that this set of vectors is linearly independent. Using these vectors as a basis, find the linear combination of training runs that results in a vector of sprint triathlon distances. Then compute her expected time. 173 10. Dava is training for a sprint triathlon consisting of a 3 mile run, followed by a 20 mile bike ride, and ending with a half mile swim. Recently, she has completed three training sessions with total times shown in the table below. 3.5 run (mi) bike (mi) swim (mi) time (min) 2 ½/₂ 35 10 1 60 0 1 65 Coordinate Spaces 205 4 Calculate Dava's expected triathlon time using two different methods. (a) Compute the rates at which Dava can expect to perform in each event (minutes per mile) assuming that all times scale linearly with distance. Then determine her total expected time. (b) Consider Dava's training run distances as vectors in R³. Show that this set of vectors is linearly independent. Using these vectors as a basis, find the linear combination of training runs that results in a vector of sprint triathlon distances. Then compute her expected time. 173