Mohsin,

The idea is, at any given time, to choose quantities to work with (time, distance, speed, etc) that will interact additively in the part of the problem you are doing.

Let A be the time taken to go upstream 1 mile and B the time taken to go downstream 1 mile. We pick this rather than speed to work with because it adds when you combine two parts of a trip.

You get two linear equations. One says 30A + 44B = 10. What is the other? Now solve them.

Now you know A and B. To find the rates of the stream and the boat you need to work with speeds, which add and subtract when you row the boat in the river. Let V be the upstream speed of the boat, W the downstream speed of the boat. Find them.

Let R be the speed of the boat, S the speed of the stream. What is V in terms of these? How about W?

Again you have two linear equations: solve & you're done.

Good Hunting!
RD