possible Angelo's kayak travels \( 15 \mathrm{~km} / \mathrm{h} \) in still water. If the river's current flows at a rate of \( 3 \mathrm{~km} / \mathrm{h} \), how long will it take to travel 33 km downstream? It will take \( \square \) hours. (Round to the nearest tenth.)

To solve the problem, we need to determine how long it will take Angelo to travel 33 km downstream in a river with a current. ### Step 1: Determine the effective speed downstream When traveling downstream, the speed of the kayak is increased by the speed of the river's current. Therefore, we can calculate the effective speed as follows: \[ v_d = v_k + v_c \] Where: - \( v_d \) = effective speed downstream - \( v_k = 15 \, \text{km/h} \) (speed of the kayak in still water) - \( v_c = 3 \, \text{km/h} \) (speed of the river's current) Substituting the values: \[ v_d = 15 + 3 = 18 \, \text{km/h} \] ### Step 2: Calculate the time to travel 33 km downstream The time taken to travel a certain distance can be calculated using the formula: \[ t = \frac{d}{v} \] Where: - \( t \) = time - \( d = 33 \, \text{km} \) (distance to travel) - \( v = 18 \, \text{km/h} \) (effective speed downstream) Substituting the values: \[ t = \frac{33}{18} \] ### Step 3: Perform the calculation Now, we will calculate the time: \[ t = \frac{33}{18} \approx 1.8333 \, \text{hours} \] ### Step 4: Round to the nearest tenth Rounding \( 1.8333 \) to the nearest tenth gives us: \[ t \approx 1.8 \, \text{hours} \] Thus, it will take approximately \( 1.8 \) hours for Angelo to travel 33 km downstream.