Question

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?

Answer 1

Speed_still = 12.25 mi/h

Speed_current = 1.75 mi/h

Explanation:

In the first trip, the motorboat goes upstream

Speed_boat = Speed_still - Speed_stream

The speed is defined as

Speed = Distance / time

This means

Speed_boat = 21 miles/ 2 h = 10.5 mi/h

Then

Speed_still - Speed_stream = 10.5 mi/h

In the second trip:

Speed_boat = Speed_still + Speed_stream

Speed_boat = 21 miles/ 1.5 h = 14 mi/h

Speed_still + Speed_stream = 14 mi/h

Then, the ystem of equations result

Speed_still + Speed_stream = 14 mi/h

Speed_still - Speed_stream = 10.5 mi/h

If we add them together

2*Speed_still = 24.5 mi/h

Speed_still = 12.25 mi/h

Speed_stream = 14 mi/h - 12.25 mi/ h = 1.75 mi/h