A motorboat that travels with a speed of 20 km/hour in still water has traveled 36 km against the current and 22 km with the current, having spent 3 hours on the entire trip. Find the speed of the current of the river.
+1253 Answer: 2 km/h
Explanation:
Let s be the speed of the current.
Let x be the time it has traveled against the current and let y be the time it traveled with the current.
Obviously, d=rt.
The rate at going against is 20-s km/hr and with is 20+s km/hr.
d=rt, or, solving for t, t = d/r.
We set t to equal x, so x = d/r.
The distance is 36, as stated, so x = 36/r
And the rate is 20-s, so x = 36/20-s.
Similarly, for y, y=22/20+s
Add those two equations to get x+y=(36/20-s)+(22/20+s).
We know that x+y=3 since the total time traveled was 3 hours.
System of equations: \(x+y=\frac{36}{20-s}+\frac{22}{20+s}, x+y=3\).
We can now solve for s. I believe that you can solve this yourself, so I won't go over the hassle.
You should eventually get s = -20/3 or 2. Obviously, only the positive number works.
Therefore, the answer is 2 km/h.
(Can somebody check this? I'm not 100% sure about it. Thanks!)
You are very welcome!
:P
+36916 Similarly:
rate x time = distance or distance/rate = time
36/(20-c) + 22/(20+c) =3
36 (20+c) + 22(20-c) = 3 (20+c)(20-c)
720 +36c +440-22c = 3 (400-c^2)
1160 +14c= 1200-3c^2
3c^2 +14c -40 =0 Using quadratic formula c = 2 km/hr
