Question

a Boat goes downstream from one place to another in 9 hours it go to the same distance upstream in 11 hours if the speed of the stream is 2 kilometre per hour find the distance between two planes​

Answer 1

Algebra Rate problems are used to find the distance traveled or time required for traveling certain distance.

Important note :  

For downstream ----> Rate of (boat /steamer) in still water + rate of stream

For upstream ----> Rate of (boat /steamer) in still water - rate of stream

With wind ----> Rate of the plane in still air + rate of the wind

against wind ----> Rate of the plane in still air - rate of the wind

1) A boat travels 30 km up a river in the same time it takes to travel 50 km down the same river. If the current of water is 5km/h . What is the speed of the boat in still water?

Solution :  

Let speed of boat in still water = x km/h  

Speed of the boat downstream = x + 5  

Speed of the boat upstream = x - 5  

Speed = Distance / time  

So time = Distance / speed

Time taken by boat to travel 30 km upstream = 30/ (x – 5)  

Time taken by boat to travel 50 km downstream = 50/ (x + 5)  

Since time taken by the boat in both cases is the same ,

 

=> 30 (x + 5) = 50 (x -5)

=> 30 x +150 = 50x -250

=> 20x = 400

=> x = 20

Thus the speed of the boat in still water is 20 km/h.

Now try to do the problem by yourself.