Question

The speed of a boat in still water is 20 km/hour. It goes 96 km upstream and return downstream to starting point in 10 hours. Find the speed of the stream.

Answer 1

Speed of the motor boat =15 km/hr
Let speed of the stream =v

Speed downstream =(15+v) km/hr
Speed upstream =(15−v) km/hr

Time taken downstream = 30(15+v)

Time taken upstream =30(15−v)

Total time = 30(15+v)+30(15−v)

Given that total time is 4 hours 30 minutes =412 hour = 92 hour

i.e., 30(15+v)+30(15−v)=92 ⇒1(15+v)+1(15−v)=92×30 ⇒1(15+v)+1(15−v)=320 ⇒15−v+15+v(15+v)(15−v)=320 ⇒30152−v2=320 ⇒30225−v2=320 ⇒10225−v2=120 ⇒225−v2=200 ⇒v2=225−200=25 ⇒v=5 km/hr

Answer 2

Answer:

We know that Time : Distance/Speed = 96/(20 + x). ⇒ x = 4. Therefore, Speed of the stream is 4 km/hr. Hope it helps!