a bout travels 280 miles downstream and back. The trip downstream took seven hours. The trip back took 14 hours. The speed of the boat in still water and the speed of the current
since distance = speed * time, if the boat's speed is b and the stream's speed is s,
7(b+s) = 280
14(b-s) = 280
b+s = 40
b-s = 20
b=30, s=10
how do you know b=30 and s=10
why is 1 equation plus and the other minus
Because (b+s) means the stream is working WITH the boat. And the current is helping the boats speed. But (b-c) means that the stream is working AGAINST the stream. So the stream is slowing the boats speed
To find the speed of the boat in still water and the speed of the current, let's assume:
- The speed of the boat in still water as 'B' (in miles per hour)
- The speed of the current as 'C' (in miles per hour)
When traveling downstream (in the same direction as the current), the effective speed of the boat is the sum of the speed of the boat in still water and the speed of the current. Hence, the downstream speed is (B + C) miles per hour.
When traveling upstream (against the current), the effective speed of the boat is the difference between the speed of the boat in still water and the speed of the current. Hence, the upstream speed is (B - C) miles per hour.
We know that the distance traveled downstream and back is 280 miles, and the time taken for the downstream trip is 7 hours, while the time taken for the upstream trip is 14 hours.
Using the formula: Speed = Distance / Time, we can set up the following equations:
For the downstream trip:
(B + C) = 280 / 7
For the upstream trip:
(B - C) = 280 / 14
Let's solve these equations to find the values of 'B' and 'C'.
Dividing 280 by 7, we get:
(B + C) = 40
Dividing 280 by 14, we get:
(B - C) = 20
Now, we have a system of equations:
B + C = 40
B - C = 20
We can solve this system of equations by adding the equations together:
(B + C) + (B - C) = 40 + 20
Simplifying:
2B = 60
Dividing by 2 on both sides:
B = 30
Now, substitute the value of B into one of the original equations to find C:
(B + C) = 40
(30 + C) = 40
Subtracting 30 from both sides:
C = 10
Therefore, the speed of the boat in still water is 30 miles per hour, and the speed of the current is 10 miles per hour.