Final answer:
By setting up two equations from the given distances and times for upstream and downstream travel, we calculated the boat's speed in still water to be 72 km/hr and the current's speed to be 20 km/hr.
Step-by-step explanation:
To find the rate of the boat in still water and the rate of the current, we can set up two equations based on the information given. When a boat travels upstream, its effective speed is reduced by the speed of the current, and when it travels downstream, its effective speed is increased by the speed of the current.
Let's denote the speed of the boat in still water as B and the speed of the current as C. The speed going upstream will then be B - C, and the speed going downstream will be B + C. The distances covered upstream and downstream are given as 416 km and 828 km, with times of 8 hours and 9 hours, respectively.
Using these variables, we can form the following equations:
- For the upstream trip, B - C = 416 km / 8 hrs = 52 km/hr
- For the downstream trip, B + C = 828 km / 9 hrs = 92 km/hr
By solving these two equations simultaneously, we can find the values of B and C. Adding the two equations will give us:
2B = 52 km/hr + 92 km/hr = 144 km/hr
Thus, the speed of the boat in still water (B) is 72 km/hr.
Subtracting the first equation from the second gives us:
2C = 92 km/hr - 52 km/hr = 40 km/hr
Therefore, the speed of the current (C) is 20 km/hr.
In conclusion, the boat's speed in still water is 72 km/hr and the current's speed is 20 km/hr.