13. A boat cruises downstream for 2 hours before heading back. It takes 3.5 hours going upstream to get back. If the speed of the stream is 8 mph, what is the speed of the boat in still water?:

a. 14.7 mph
b. 19.6 mph
c. 24.8 mph
d. 29.3 mph

See if you can explain my equation to yourself

3.5(x-8) = 2(x+8) then solve it, I got d)

To determine the speed of the boat in still water, we need to use the concept of relative velocity. Let's break down the problem step by step:

1. Let's denote the speed of the boat in still water as 'x' mph.
2. The speed of the stream is given as 8 mph.
3. When the boat travels downstream (with the current), its effective speed is the sum of its speed in still water and the speed of the stream. Therefore, the boat's speed downstream is (x + 8) mph.
4. The time taken to travel downstream is given as 2 hours.
5. When the boat travels upstream (against the current), its effective speed is the difference between its speed in still water and the speed of the stream. Therefore, the boat's speed upstream is (x - 8) mph.
6. The time taken to travel upstream is given as 3.5 hours.
7. Since we know that distance equals speed multiplied by time, we can set up two equations based on the distances traveled upstream and downstream:
- Distance downstream = (x + 8) mph * 2 hours
- Distance upstream = (x - 8) mph * 3.5 hours
8. Since the distance traveled downstream and upstream is the same, we can equate the two equations and solve for 'x':

(x + 8) * 2 = (x - 8) * 3.5

9. Multiplying out, we get:

2x + 16 = 3.5x - 28

10. Simplifying, we find:

1.5x = 44

11. Dividing both sides by 1.5, we get:

x = 44 / 1.5 = 29.3 mph

So, the speed of the boat in still water is 29.3 mph. Therefore, the correct answer is option d: 29.3 mph.