11:18 C $5 G+$ 154) Quiz (i) (D) One solution Question 4 1 Point A boat travels 30 miles downstream in 2 hours and it takes 4 hours to travel back upstream. What is the speed of the boat if it were in still water and what is the speed of the river current? (A) The boat's speed is 30 miles per hour and the current speed of the river is 0 miles per hour (B) The boat's speed is 15 miles per hour and the current speed of the river is 5 miles per hour (C) The boat's speed is 23 miles per hour and the current speed of the river is 7 miles per hour (D) The boat's speed is 11.25 miles per hour and the current speed of the river is 3.75 miles per hour Last saved 11:17:31 PM Questions Filter (15) Save and Close Submit $A A$ learning.rasmussen.edu C

Step 1 ：Let's denote the speed of the boat in still water as \(b\) and the speed of the river current as \(c\).

Step 2 ：When the boat is moving downstream, the speed of the boat and the current add up. So, the downstream speed is \(b + c\).

Step 3 ：When the boat is moving upstream, the speed of the boat is reduced by the speed of the current. So, the upstream speed is \(b - c\).

Step 4 ：We know that speed is distance divided by time. So, we can write the downstream speed as \(\frac{30}{2} = 15\) miles per hour and the upstream speed as \(\frac{30}{4} = 7.5\) miles per hour.

Step 5 ：Setting these equal to our expressions for downstream and upstream speed, we get the equations \(b + c = 15\) and \(b - c = 7.5\).

Step 6 ：Solving this system of equations, we find that \(b = 11.25\) miles per hour and \(c = 3.75\) miles per hour.

Step 7 ：Final Answer: The boat's speed in still water is \(\boxed{11.25}\) miles per hour and the speed of the river current is \(\boxed{3.75}\) miles per hour.