Mathematics

Question

brian is in a 100 mile bike race. he needs to average 12.5 mph if he wants to complete the race before it ends. in a practice ride he biked 60 miles. for the first 30 miles his average speed was 16 mph. for the next 30 miles his average was 15 mph. if he mathes these speeds for the first 60 miles then rest 1 hour . what speed should he maintain rounded to the nearest integer for the last 40 miles to complete the race in time

1 Answer

  • Answer:

    Brian needs to complete the 100 mile bike race in a time of 100 miles / (12.5 mph) = 8 hours.

    He has already ridden for a distance of 60 miles, so he has a time of 8 hours * (60 miles / 100 miles) = 4.8 hours to complete the remaining 40 miles.

    His average speed for the first 39 miles was 16 mph, so he rode this distance in a time of 39 miles / (16 mph) = 2.44 hours.

    His average speed for the next 39 miles was 15 mph, so he rode this distance in a time of 39 miles / (15 mph) = 2.6 hours.

    The total time he has spent on the first 60 miles is 2.44 hours + 2.6 hours = 5.04 hours.

    If he takes a 1 hour break, he has a total of 4.8 hours - 5.04 hours + 1 hour = 0.76 hours left to ride the last 40 miles.

    To complete the race in time, Brian needs to maintain a speed of 40 miles / 0.76 hours = 52.63 mph. Rounded to the nearest integer, this is 53 mph.

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