Final answer:
The student must set up two equations that represent the time it takes to travel a certain distance downstream and upstream, equate them, and solve for the unknown current of the river.
Step-by-step explanation:
The student is asked to find the current of the river given that a sight-seeing boat travels 2.9 miles downstream and 1.6 miles upstream in the same amount of time. To solve this, we first need to establish the equations for the time taken to travel downstream and upstream, which are based on the boat's calm water speed and the unknown river current.
Let's denote the river's current speed as 'c'. The speed of the boat downstream will be (19+c) mph and upstream will be (19-c) mph. The time 't' it takes for both the downstream and upstream trips is equal, so we can set up the following equations:
Downstream: \(\frac{2.9}{19+c} = t\)
Upstream: \(\frac{1.6}{19-c} = t\)
Setting the two expressions for 't' equal to each other gives us:
\(\frac{2.9}{19+c} = \frac{1.6}{19-c}\)
Cross-multiplying and solving for 'c' gives us the speed of the current.