You'll certainly fill the bucket faster with both taps on than you will just using one tap, so t < c < h must be true. So I) is definitely true, and II) is definitely false. Now, c/2 is the time it would take two cold taps to fill the bucket. We don't have two cold taps -- we have one cold tap, and one slower tap. So t > c/2. Similarly, h/2 is how long it would take two hot taps. We don't have two hot taps -- we have one hot tap, and one faster tap. So t < h/2. So III) must also be true.
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