A man swim at a speed of 50m/min, swims 100m against the current and 100m with the current. if the time difference between the two times is 3min 45sec. find the speed of the current?
since time = distance/speed,
100/(50-x) = 100/(50+x) + 3.75
Now just find x.
In general, distance = rate x time
This case:
distance = (rate + current) x time
distance = (rate - current) x time
100 = (50 -c)(t)
100 = (50+c) (t + 3 3/4 minutes)
This should get you started.
You got your speeds reversed, John.
The slower speed takes longer.
To find the speed of the current, we need to set up an equation based on the given information.
Let's denote the speed of the current as 'c' (in m/min).
The man's swimming speed is given as 50m/min.
When he swims against the current, his effective speed decreases by the speed of the current. So, the time it takes for him to swim 100m against the current is 100 / (50 - c) minutes.
When he swims with the current, his effective speed increases by the speed of the current. So, the time it takes for him to swim 100m with the current is 100 / (50 + c) minutes.
According to the given information, the time difference between these two swims is 3 minutes and 45 seconds, which is equal to 3 + 45/60 = 3.75 minutes.
So, we can set up the equation as follows:
100 / (50 - c) - 100 / (50 + c) = 3.75
Now, we can solve this equation to find the value of 'c'.
To solve the equation, we can simplify it by multiplying both sides by (50 - c)(50 + c) to get rid of the denominators:
100 * (50 + c) - 100 * (50 - c) = 3.75 * (50 - c)(50 + c)
Simplifying further:
5000 + 100c - 5000 + 100c = 3.75(2500 - c^2)
200c = 3.75(2500 - c^2)
Dividing both sides by 200:
c = 0.01875(2500 - c^2)
Now, we have a quadratic equation. To solve it, we can simplify the equation further:
c = 0.01875(2500 - c^2)
c = 46.875 - 0.01875c^2
0.01875c^2 + c - 46.875 = 0
Now, we can solve this quadratic equation using various methods, such as factoring or the quadratic formula. Let's use the quadratic formula:
c = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 0.01875, b = 1, and c = -46.875
Substituting these values into the formula:
c = (-1 ± √(1^2 - 4 * 0.01875 * -46.875)) / (2 * 0.01875)
Simplifying further:
c = (-1 ± √(1 + 3.75)) / 0.0375
c = (-1 ± √4.75) / 0.0375
Now, calculating the two possible values for 'c':
c = (-1 + √4.75) / 0.0375 ≈ 0.140
c = (-1 - √4.75) / 0.0375 ≈ -6.173
Since the speed of the current can't be negative, the speed of the current is approximately 0.14 m/min.