Question

Roberto, Christopher, and Levi are amateur cyclist riding in the 165.1 km long Tour of Cortez bicycle race. Each cyclist is individually timed in the event.

Two hours into his race, Roberto has completed 73.4 km.

Three hours into his race, Christopher has completed 112.6 km.

Three and a half hours into his race, Levi has completed 128.2 km.

The cyclist must complete the race in under 260 minutes to qualify for the professional cyclist series for the upcoming year.

Place the cyclist in order from the least average minutes per km to the greatest average minutes per km that they need ride for the remainder of the race to qualify for the professional cyclist series.

Answer 1

what names would be first , second and third because i am having a hard time with this question

Answer 2

this is a bit tedious but ultimately not too bad of a question

first we convert 260min to hours by dividing by 60 mins
260 / 60 = (13/3) hours. I'm just gonna leave this as a fraction for now.

each racer needs 165.1km total

so robert needs (165.1 - 73.4)km because he's already done 73.4 km
Christopher needs (165.1-112.6) km.
Levi has completed (165.1-128.2) km.

Robert has already used up 2 hours out of the 13/3 allotted hours, so he has (13/3 - 2) hours to complete the race
same logic, Christopher has (13/3-3) hours
Levi has (13/3-3.5) hours left

Answer 3

now, to find the time each racer needs to complete the race, simply divide that racer's miles to go over the hours they have left

Robert ---> (165.1 - 73.4) / (13/3 - 2)
Christopher ---> (165.1-112.6) / (13/3-3)
Levi ---> (165.1-128.2) / (13/3-3.5)
evaluate these, be very careful about order of operations. you may want to simplify each set of parentheses first before doing the division.