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A boat capsized and sank in a lake. Based on an assumption of a mean weight of [tex]137 \, \text{lb}[/tex], the boat was rated to carry 50 passengers, making the load limit [tex]6,850 \, \text{lb}[/tex].

a) How much weight did the boat initially assume each passenger would weigh?

b) By how much did the passengers' weight exceed the initial assumption when the boat capsized?

Answer :

Final answer:

The boat initially assumed each passenger would weigh 137lb. When it capsized, it was carrying passengers that in total weighed 2,750 lb more than its original load limit.

Explanation:

To answer these questions, we can use the given data to perform a series of simple calculations. For question (a), the weight the boat initially assumed for each passenger was 137 lb. This is given directly in the problem statement.

For question (b), we need to know that the boat's load limit was 6,850 lb, it carried 60 passengers with an average weight of 160 lb. So, the total weight of all passengers on the boat was 60 passengers times 160 lb/passenger, or 9,600 lb. This exceeds the boat's original load limit by the difference of 9,600 lb and 6,850 lb, which is 2,750 lb.

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