Question

The speed of a stream is 3 km per hour. A boat travels upstream 12 km and then returns to its original position downstream along the same route. If the speed of the boat in still water is 9 km per hour, what is the average speed of the boat for the entire round trip?

Answer 1

Answer:

7 km

Step-by-step explanation:

let the speed of boat in still water is x km/hr. 

given speed of stream is 3 km/hr. 

then speed of boat upstream = ( x - 3) km/hr

speed of boat downstream = (x + 3 ) km/hr 

Distance travelled upstream = 4 km

time taken to travel upstream = distance travelled upstream / speed of boat 

upstream

= 4 / (x - 3 ) .............(1) 

Distance travelled downstream = 10 km

time taken to travel downstream = distance travelled downstream / speed of boat 

downstream

= 10 / (x + 3) ............(2)

given that boat takes same time to travel upstream and downstream.i.e; (1) & (2) are equal

i.e. 4/(x-3) = 10/ (x + 3 ) 

4 * (x +3 ) = 10 * (x- 3)

4x + 12 = 10x - 30

12 + 30 = 10x -4x 

42 = 6x 

x = 42 / 6 = 7. 

i.e speed of boat in still water is 7 km/hr.