It seems to me that there are multiple solutions because the exercise does not tell us how the two calorie-burning rates are related. Alternatively, they could have given us the total minutes spent exercising. Then we could narrow it down to a specific solution.

For examples:

LI rate of 9-1/2 cal/min --> 10 min HI + 20 min LI = 320 calories

LI rate of 6-5/6 cal/min --> 12 min HI + 24 min LI = 320 calories

LI rate of 4-1/6 cal/min --> 15 min HI + 30 min LI = 320 calories

LI rate of 3-1/2 cal/min --> 16 min HI + 32 min LI = 320 calories

LI rate of 1-1/2 cal/min --> 20 min HI + 40 min LI = 320 calories

There are many other possibilities; how can we know which one they're talking about?

If they had included a statement like, "Total exercise time is 36 min", then we could give a specific answer.

If they had included a statement like, "The ratio of HI rate to LI rate is 26:3", then we could give a specific answer.