A boat traveled 210 miles downstream and back. The trip downstream took 10 hours. The trip back took 70 hours. What is the speed of the boat in still water. What is the speed of the current?
If the boat's speed is b and the current's speed is c, then since distance = speed * time,
10(b+c) = 210
70(b-c) = 210
Now just solve for b and s.
20
To find the speed of the boat in still water and the speed of the current, let's start by defining some variables.
Let's say the speed of the boat in still water is "b" (in miles per hour) and the speed of the current is "c" (also in miles per hour).
When the boat travels downstream (with the current), its effective speed will be the sum of the boat's speed in still water and the speed of the current, so we can write the equation:
Effective speed downstream = b + c
Given that the boat traveled 210 miles downstream in 10 hours, we can create another equation:
Effective speed downstream = Distance / Time
b + c = 210 / 10
Simplifying this equation, we have:
b + c = 21
When the boat travels upstream (against the current), its effective speed will be the difference between the boat's speed in still water and the speed of the current, so we can write the equation:
Effective speed upstream = b - c
Given that the boat traveled the same distance of 210 miles upstream in 70 hours, we can create another equation:
Effective speed upstream = Distance / Time
b - c = 210 / 70
Simplifying this equation, we have:
b - c = 3
Now, we have a system of two equations with two unknowns:
b + c = 21
b - c = 3
We can solve this system of equations to find the values of "b" and "c".
Adding both equations together, we get:
(b + c) + (b - c) = 21 + 3
2b = 24
b = 12
Substituting the value of "b" back into one of the original equations, we find:
12 + c = 21
c = 9
Therefore, the speed of the boat in still water is 12 miles per hour, and the speed of the current is 9 miles per hour.