A conveyor belt moves bottles at a constant speed

Hi jjjinapinch,

We're told that a conveyor belt moves bottles at a constant speed of 120 centimeters per second (from a loading dock to an unloading dock). We're asked if the distance that the conveyor belt moves a bottle is less than 90 meters? (1 meter = 100 centimeters). This is a YES/NO question.

This prompt is clearly a 'rate' question, but it also is a 'unit conversion' question. You get to choose how you want to 'convert' the units - into either meters or centimeters and you can decide whether you want to use minutes or seconds. I'm going to convert the information into meters and seconds. To start, 120 centimeters = 1.2 meters

1) It takes the conveyor belt LESS than 1.2 minutes to move the bottle from the loading dock to the unloading dock.

Here, I'm going to convert 1.2 minutes into seconds...
(1 2/10)(60) = 60 + 12 = 72 seconds

Thus, we know that the conveyor belt spent LESS than 72 seconds moving each bottle. Thus, the distance that each bottle was moved was LESS than ... (72 seconds)(1.2 meters/second) = 86.4 meters
By extension, the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

2) It takes the conveyor belt MORE than 1.1 minutes to move the bottle from the loading dock to the unloading dock.

With this information, we can determine the distance that each bottled moved at the MINIMUM...
(1 1/10)(60) = 60 + 6 = 66 seconds
(66 seconds)(1.2 meters/second) = MORE than 79.2 meters .
IF... the distance was 80 meters, then the answer to the question is YES.
IF... the distance was 100 meters, then the answer to the question is NO.
Fact 2 is INSUFFICIENT

Final Answer: A
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