Question

The first day Rita participates in a biathlon, she jogs at a rate of 6 miles/hour and bikes at a rate of 10 miles/hour. She covers a total of 26 miles that day. The second day, she continues to jog at a rate of 6 miles/hour, but a hamstring pull slows her biking rate to 5 miles/hour. The second day she covers a total of 22 miles. If she jogged the same number of hours (x) and biked the same number of hours (y) both days, how many hours did she bike each day?

Answer 1

Answer: she biked 0.8 hour each day

Step-by-step explanation:

Let x represent the number of hours that she jogged on both days.

Let y represent the number of hours that she biked on both days.

Distance = speed × time

On the first day, she jogs at a rate of 6 miles/hour and bikes at a rate of 10 miles/hour. She covers a total of 26 miles that day. This is expressed as

6x + 10y = 26- - - - - - - - - - - - - - - 1

The second day, she continues to jog at a rate of 6 miles/hour, but a hamstring pull slows her biking rate to 5 miles/hour. The second day she covers a total of 22 miles. This means that

6x + 5y = 22- - - - - - - - - - - -2

Subtracting equation 2 from equation 1, it becomes

5y = 4

y = 4/5 = 0.8

Substituting y = 0.8 into equation 1, it becomes

6x + 10(0.8) = 26

6x + 8 = 26

6x = 26 - 8 = 18

x = 18/6

x = 3