speed problem

[mija]

a boat takes 5 hours to go 300km downstream. It takes the same time to go 150km uppstream. What is
speed of boat in still water and speed of stream ?

Ans :45km/hr,15 km/hr

please explain the 2 equations formed here ?

[fibbonnaci]

the speed is a mix of both the speed of the boat and the stream

now when a boat travels downstream, the speed of the boat is influenced by the speed of the stream such that the sppeds add up.

so, Distance/time = speed

x-> speed of the stream and y-> speed of the boat.

Downstream,
300/5 = x+y
so, x +y = 60 -> 1

Upstream,
150/5 = x-y [note: when a boat travels against the stream, its speed decreases]

so x-y = 30 ->2

solving these simultaneous equations we get x= 45km/hr and y=15km/hr.

Hope this helps!

[mbsachi]

Let A be the speed of the boat alone (without considering stream effect)
And B, the speed of stream alone.

Speed = Distance/Time

Downstream:
A + B = 300/5 = 60 km/h
Upstream:
A - B = 150/5 = 30 km/h

Solving these 2 equations:
A = 45 km/h
B = 15 km/h

Speed of boat in still water = A = 45 km/h
Speed of stream alone = B = 15 km/h

[suryapal]

speed *time = distance

(B+S)*5= 300 ( where B is the speed of boat and S is the speed of stream)
and
(B-S)*5 = 150

on solving both equation we get the requires answer.. i.e B = 45 and S=15