To solve this problem, consider two functions: {{CMD_129}} {{CMD_130}} {{MATH_131}} the amount of water in Roxy's bowl at time {{MATH_132}}. {{CMD_133}} {{MATH_134}} the amount of water in Yuri's bowl at time {{MATH_135}}. {{CMD_136}} Now if {{MATH_137}} is the time the cats start drinking and {{MATH_138}} is the time the cats finish drinking. Then we have {{MATH_139}} and {{MATH_140}} Since the amount of water in a bowl at time {{MATH_141}} is a continuous function, as water is ``lapped'' up in continuous amounts, {{MATH_142}} is a continuous function, and hence the Intermediate Value Theorem applies. Since {{MATH_143}} is positive when at {{MATH_144}} and negative at {{MATH_145}}, there is some time {{MATH_146}} when the value is zero, meaning {{MATH_147}} meaning there is the same amount of water in each of their bowls. {{CMD_148}} {{CMD_149}}