Alana was working out on the treadmill. she worked out for 15 minutes. part of the time she was walking at 3.1 miles per hour. the rest of the time she was jogging at 5.2 miles per hour. during the 15 minutes, she covered exactly 1.09 mile. how much time did she spend walking, and how much time jogging

Time taken for work out was 1/4 hours
let the time taken to walk be x
time spent for jogging will be (1/4-x)

distance=speed×time

distance walked will be:
3.1x miles

distance jogged will be:
5.2(1/4-x) miles

Total distance:
3.1x+5.2(1/4-x)=1.09

solving for x we get
3.1x-5.2x+1.3=1.09
2.1x=0.21
x=0.1
Thus time spent on waling was o.1 hours
time spent on jogging was 0.25-0.1=0.15 hours