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
