Problem 926

To get to a cabin, Dana can ride a bicycle west from a parking lot along the edge of a rectangular reservoir for 2.4 miles, and then south along the edge for 0.7 miles. Or she can row a boat directly from the parking lot. If Dana can ride 1.2 times as faster as she can row, which is the faster route?




Let the variable c represent the distance that Dana would have to row to reach the cabin. This distance is the hypotenuse of a right triangle whose sides are length 2.4 miles and 0.7 miles.

c2  = (2.4 mi)2 + (0.7 mi)2

c2 = 5.76 mi2 + 0.49 mi2

= 6.25 mi2

c =\sqrt{6.25 mi^{2}}

= 2.5 mi

Determine how far she could ride her bicycle in the same amount of time it takes her to row 2.5 miles. Use the fact that she can ride 1.2 times as fast as she can row.

2.5 miles * 1.2 = 3 miles

Compare this number to total distance that Dana would have to ride on her bicycle to get to the cabin,

2.4 miles + 0.7 miles = 3.1 miles

Since 3.1 miles is greater than 3 miles, the faster way to the cabin is rowing a boat.


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