a motorboat takes 5 hours to travel 150 Miles going Upstream. the return trip takes 3 hours going Downstream .what is the rate of the boat in still water and what is the rate of the current ?

Speed of boat in still water = 40 mph

Rate of current = 10 mph

Step-by-step explanation:

Let the speed of boat in still water be x & let the speed of the stream be y.

Total Distance = 150 miles

Time taken to travel during upstream = 5 hrs

Speed of the boat during upstream =

Speed of boat during upstream can be represented as because the boat is moving in the opposite direction of flow of stream.

Time taken to travel during downstream = 3 hrs

Speed of boat during downstream =

Speed of boat during downstream can be represented as because the boat is moving in the same direction of flow of stream.

We got a pair of linear eqns. Let   be eqn.1 and be eqn.2 . Using substitution method ,

From eqn.1 ,

Putting 'x' in eqn.2 ,

Putting y in eqn.1 ,

Hence , the speed of boat in still water is 40 mph and speed of stream is 10 mph

step-by-step :