A girl rows 11 km downstream in 2 h. Her return trip takes 4 h. How fast is the current. in km/h?
What is phisecs, some small unit of time?
rowing rate --- x km/h
current rate --- y km/h
A girl rows 11 km downstream in 2 h
---> 2(x+y) = 11
2x + 2y = 11
"Her return trip takes 4 h"
---> 4(x-y) = 11
4x - 4y = 11
first times 2
4x + 4y = 22
add to the 2nd
8x = 33
x = 33/8 km/h
y = (11 - 2(33/8)/2 = 11/8
the current speed is 11/8 km/h
check:
downstream:
2(33/8+11/8) = 2(5.5) = 11
upstream:
4(33/8 - 11/8) = 4(2.75) = 11
My answer is correct!
thank you so much !!!
To find the speed of the current, we can set up a system of equations based on the given information.
Let's assume the speed of the girl's rowing boat is "x" km/h, and the speed of the current is "y" km/h.
When rowing downstream (with the current), the effective speed of the girl's boat is increased by the speed of the current, so her speed becomes (x + y) km/h.
According to the given information, the girl rows 11 km downstream in 2 hours. Therefore, we can write the equation:
Distance = Speed × Time
11 km = (x + y) km/h × 2 h
Simplifying this equation, we get:
11 = 2(x + y) (equation 1)
Similarly, when rowing upstream (against the current), the effective speed of the girl's boat is decreased by the speed of the current, so her speed becomes (x - y) km/h.
The return trip takes 4 hours, so we can set up another equation:
Distance = Speed × Time
11 km = (x - y) km/h × 4 h
Simplifying this equation, we get:
11 = 4(x - y) (equation 2)
Now we have a system of two equations with two variables. We can solve these equations simultaneously to find the values of x and y.
Let's solve equations 1 and 2:
11 = 2x + 2y (equation 1)
11 = 4x - 4y (equation 2)
We can solve this system of equations by eliminating one variable. Let's multiply equation 1 by 2 and equation 2 by -1:
22 = 4x + 4y (equation 1, multiplied by 2)
-11 = -4x + 4y (equation 2, multiplied by -1)
Now, we can add the two equations:
22 + (-11) = (4x + 4y) + (-4x + 4y)
11 = 8y
Dividing both sides by 8, we get the value of y (the speed of the current):
y = 11/8
y = 1.375 km/h
Therefore, the speed of the current is 1.375 km/h.