Question

A boat goes 30km upstream and 20 km downstream in 7 hours.in 6 hours it can go 18km upstream and 30 km downstream.determine the speed of the stream and that of the boat in still water

Answer 1

hey dude ..
I think the question is wrong because in the above sentence it is written that the boat goes 30 km upstream and 20 km down stream in same time i.e. 7hrs 
but how it is possible ... boat generally have more speed in downstream
sorry dude plz check your question and .. ask me in the comment box

Answer 2

Answer:

Speed of the boat = 8 km/hr

Speed of the water = 2 km/hr

Step-by-step explanation:

Let the speed of boat be x km/h and the speed of stream be y km/h

Now, Speed of upstream = x - y

Speed of downstream = x + y

According to the given condition,

$\frac{30}{x-y}+\frac{20}{x+y} = 7\\\\and, \frac{18}{x-y}+\frac{30}{x+y} = 6\\\\\text{Let }\frac{1}{x-y}=a\text{ and } \frac{1}{x+y}=b \\\\\implies30\cdot a + 20\cdot b = 7.............(1)\\\\18\cdot a + 30\cdot b=6...........(2)\\\\\text{Multiplying equation 1 by 3 and equation 2 by 5 and subtracting the resultant equations}\\\\\text{We get, }b= \frac{1}{10}=\frac{1}{x+y}\\\\\implies a = \frac{1}{6} =\frac{1}{x-y}$

So, x + y = 10

and, x - y = 6

Now, on solving above equations,

We obtain x = 8 and y = 2

Hence, Speed of the boat = 8 km/hr

Speed of the water = 2 km/hr