A boat has a speed of 5 mph in calm water. It takes the boat 3 hours to travel upstream but only 2 hours to travel the same distance downstream. Using the data in the table, what is the value of c, the speed of the current? Distance (mi) Rate (mph) Time (hr) Upstream 3 times open paren 5 minus c close paren open paren 5 minus c close paren 3 Downstream 2 times open paren 5 plus c close paren open paren 5 plus c close paren 2
The distances are equal, so set the upstream distance equal to the downstream distance: 3(5 − c) = 2(5 + c). Expanding gives 15 − 3c = 10 + 2c, so 5 = 5c and c = 1 mph. The current’s speed is 1 mph, choice B.
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