Question

List the independent and dependent variables for each situation:

Answer 1

Part (a)

Independent variable = age
Dependent variable = height

"depends on age" indicates that age is independent. 

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Part (b)

Independent variable = amount of sleep
Dependent variable = mood

The key word is "determines". The stuff before this word is the independent variable which affects the dependent variable.
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Part (c)

Independent variable = time water has been running
dependent variable = amount of water in the tub

Time is usually the independent variable
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Part (d)

Independent variable = speed
dependent variable = distance from home

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Part (e)

Independent variable = amount of homework done
dependent variable = speed

This seems like an odd pairing of homework and speed. Could there be a typo? I noticed that part (f) is very similar

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Part (f)

Independent variable = amount of hw that is assigned
dependent variable = amount of homework done

Like with part (a), the stuff before "depends" is the dependent variable