With her motorboat at full speed Dawn gets to her fishing hole, which is 21 miles upstream, in 2 hours. The return trip takes 1.5 hours. How fast could her motorboat go in still water? What is the rate of the current?
Accepted Solution
A:
Answer:Speed_still = 12.25 mi/hSpeed_current = 1.75 mi/hStep-by-step explanation:In the first trip, the motorboat goes upstreamSpeed_boat = Speed_still - Speed_streamThe speed is defined asSpeed = Distance / timeThis meansSpeed_boat = 21 miles/ 2 h = 10.5 mi/hThenSpeed_still - Speed_stream = 10.5 mi/hIn the second trip:Speed_boat = Speed_still + Speed_streamSpeed_boat = 21 miles/ 1.5 h = 14 mi/hSpeed_still + Speed_stream = 14 mi/hThen, the ystem of equations resultSpeed_still + Speed_stream = 14 mi/hSpeed_still - Speed_stream = 10.5 mi/hIf we add them together2*Speed_still = 24.5 mi/hSpeed_still = 12.25 mi/hSpeed_stream = 14 mi/h - 12.25 mi/ h = 1.75 mi/h