A riverboat travels 75 km downstream in 3 hours. It travels 84 km upstream in 4 hours. Find the speed of the boat and the speed of the stream. The speed of the boat is \( \square \) and the speed of the stream is \( \square \)

To find the speed of the boat and the speed of the stream, we can set up the problem using the following variables: - Let \( b \) be the speed of the boat in still water (in km/h). - Let \( s \) be the speed of the stream (in km/h). When the boat is traveling downstream, its effective speed is \( b + s \), and when it is traveling upstream, its effective speed is \( b - s \). From the problem, we have the following information: 1. The boat travels 75 km downstream in 3 hours. 2. The boat travels 84 km upstream in 4 hours. We can use the formula for speed, which is: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \] ### Step 1: Set up the equations **Downstream:** \[ b + s = \frac{75 \text{ km}}{3 \text{ hours}} = 25 \text{ km/h} \] **Upstream:** \[ b - s = \frac{84 \text{ km}}{4 \text{ hours}} = 21 \text{ km/h} \] ### Step 2: Solve the system of equations Now we have the following system of equations: 1. \( b + s = 25 \) (Equation 1) 2. \( b - s = 21 \) (Equation 2) We can solve these equations by adding them together: \[ (b + s) + (b - s) = 25 + 21 \] \[ 2b = 46 \] \[ b = 23 \text{ km/h} \] Now, we can substitute \( b \) back into one of the equations to find \( s \). Using Equation 1: \[ 23 + s = 25 \] \[ s = 25 - 23 = 2 \text{ km/h} \] ### Conclusion The speed of the boat is \( 23 \) km/h and the speed of the stream is \( 2 \) km/h. Thus, the final answers are: - The speed of the boat is \( 23 \) km/h. - The speed of the stream is \( 2 \) km/h.