A man swimming in a river finds that it takes him thrice the time to swim 2 km upstream as it takes him to swim bac. If the river flows at the rate of 1.5 km/hr, find the swimming speed of the man in still water.

since time = distance/speed,

2/(s-1.5) = 3 * 2/(s+1.5)

To solve this problem, we need to understand the concept of relative velocity.

Let's assume that the swimming speed of the man in still water is 'V' km/hr.
When swimming upstream, the speed of the man will be reduced by the speed of the river's flow, which is 1.5 km/hr.
So, the effective speed of the man while swimming upstream is (V - 1.5) km/hr.

Now, according to the problem, it takes the man thrice the time to swim 2 km upstream as it takes him to swim back, i.e., downstream.

Let's say the time taken to swim downstream is 't' hours.
Therefore, the time taken to swim upstream would be 3t hours.

Now, using the formula Distance = Speed × Time:

Distance upstream = (V - 1.5) × (3t) [as distance = speed × time]
Distance downstream = (V + 1.5) × t

We know that distance = 2 km in both cases, so we can form the equation:

(V - 1.5) × (3t) = 2
(V + 1.5) × t = 2

Simplifying the equations, we get:

3Vt - 4.5t = 2
Vt + 1.5t = 2

Now, we have two equations with two variables (V and t).
Solving these equations simultaneously, we can find the values of V and t.

Let's solve the equations:

From the second equation, we can express t in terms of V:
t = 2/(V + 1.5)

Substituting this value of t into the first equation:
3V(2/(V + 1.5)) - 4.5(2/(V + 1.5)) = 2

Simplifying further:
6V/(V + 1.5) - 9/(V + 1.5) = 2

Now, we can combine the fractions on the left side:
(6V - 9)/(V + 1.5) = 2

Cross-multiplying:
6V - 9 = 2(V + 1.5)

Expanding and simplifying:
6V - 9 = 2V + 3
6V - 2V = 3 + 9
4V = 12
V = 12/4
V = 3

Therefore, the swimming speed of the man in still water is 3 km/hr.