The speed of the boat is \( \square \) A riverboat travels 84 km downstream in 3 hours. It travels 88 km upstream in 4 hours. Find the speed of the boat and the speed of the stream.

To find the speed of the boat in still water 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 84 km downstream in 3 hours. 2. The boat travels 88 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:** \[ b + s = \frac{84 \text{ km}}{3 \text{ hours}} = 28 \text{ km/h} \] **Upstream:** \[ b - s = \frac{88 \text{ km}}{4 \text{ hours}} = 22 \text{ km/h} \] ### Step 2: Write the system of equations We now have the following system of equations: 1. \( b + s = 28 \) (1) 2. \( b - s = 22 \) (2) ### Step 3: Solve the system of equations We can add equations (1) and (2) to eliminate \( s \): \[ (b + s) + (b - s) = 28 + 22 \] \[ 2b = 50 \] \[ b = 25 \text{ km/h} \] Now, we can substitute \( b = 25 \) back into one of the original equations to find \( s \). We'll use equation (1): \[ 25 + s = 28 \] \[ s = 28 - 25 = 3 \text{ km/h} \] ### Conclusion The speed of the boat in still water is \( \boxed{25} \) km/h, and the speed of the stream is \( \boxed{3} \) km/h.