Current of the water is 1.714 mph
<h3><u>Solution:</u></h3>
Given that,
A boat travels 12 Mph in still water
It can travel 18 miles upstream in the same time that it can travel 24 miles downstream
To find: current of water
<u><em>Formula to remember:</em></u>
If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then:
Speed downstream = (u + v) km/hr
Speed upstream = (u - v) km/hr
Let "t" be the time taken for upstream and downstream
Let "x" be the speed of stream or current
<u><em>For upstream:</em></u>
distance = 18 miles
time taken = t
speed in still water = 12 mph
speed of stream = "x"
we know that : ![speed = \frac{distance}{time}](https://tex.z-dn.net/?f=speed%20%3D%20%5Cfrac%7Bdistance%7D%7Btime%7D)
![12 - x = \frac{18}{t} ---- eqn 1](https://tex.z-dn.net/?f=12%20-%20x%20%3D%20%5Cfrac%7B18%7D%7Bt%7D%20----%20eqn%201)
<u><em>For downstream:</em></u>
distance = 24 miles
time taken = t
speed in still water = 12 mph
speed of stream = "x"
![12 + x = \frac{24}{t} ---- eqn 2](https://tex.z-dn.net/?f=12%20%2B%20x%20%3D%20%5Cfrac%7B24%7D%7Bt%7D%20----%20eqn%202)
Now, adding those two equations (1) and (2) we get,
![12 - x + 12 + x = \frac{18}{t} + \frac{24}{t}\\\\24 = \frac{18}{t} + \frac{24}{t}\\\\24t = 18 + 24\\\\24t = 42\\\\t = \frac{42}{24}\\\\t = \frac{7}{4}](https://tex.z-dn.net/?f=12%20-%20x%20%2B%2012%20%2B%20x%20%3D%20%5Cfrac%7B18%7D%7Bt%7D%20%2B%20%5Cfrac%7B24%7D%7Bt%7D%5C%5C%5C%5C24%20%3D%20%5Cfrac%7B18%7D%7Bt%7D%20%2B%20%5Cfrac%7B24%7D%7Bt%7D%5C%5C%5C%5C24t%20%3D%2018%20%2B%2024%5C%5C%5C%5C24t%20%3D%2042%5C%5C%5C%5Ct%20%3D%20%5Cfrac%7B42%7D%7B24%7D%5C%5C%5C%5Ct%20%3D%20%5Cfrac%7B7%7D%7B4%7D)
<h3>t = 1.75 hours</h3>
Now, from equation (1) we get
![12 - x = \frac{18}{1.75}\\\\12 - x = 10.29\\\\x = 12 - 10.29\\\\x = 1.71](https://tex.z-dn.net/?f=12%20-%20x%20%3D%20%5Cfrac%7B18%7D%7B1.75%7D%5C%5C%5C%5C12%20-%20x%20%3D%2010.29%5C%5C%5C%5Cx%20%3D%2012%20-%2010.29%5C%5C%5C%5Cx%20%3D%201.71)
Thus current of the water is 1.71 mph