# Upstream & Downstream

• Concepts:

Downstream: In water the direction along the stream
Upstream: In water the direction against the stream

Let the speed of a boat in still water is x km/hr and the speed of the stream is y km/hr.
Downstream speed, d = (x+y) km/hr
Upstream speed, u = (x-y) km/hr
Speed of boat in still water, x = 1/2(d+u) km/hr
Speed of stream , y = 1/2(d-u) km/hr

Questions

Ram’s speed is with the current is 10 m/s and speed of current is 2 m/s .Then What’s Ram’s speed against current?

Let speed of current y = 2 m/s
Let Ram’s speed in still water is x m/s
x+2 = 10 m/s
x = 8 m/s

A boat can travel with a speed of 15 m/s in still water. If the speed of the stream is 5 m/s, find the time taken by the boat to go 100 m downstream?

x = 15 m/s
y= 5 m/s
downstream speed ,d = 15+5 = 20 m/s
distance = 100 m
time taken = 100/20 = 5seconds

A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours and 30 minutes. Find the speed of the stream?

x = 15 km/hr
t = 4 1/2 h = 9/2 hours
9/2 = 30/15+y + 30/15 - y where y is speed of stream
9/2 = 30(30)/225-y^2
225-y^2 = 900*2/9 = 200
y^2 = 25
y = 5 km/hr

A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?

D/x-y = 8 4/5 = 44/5
D/x+y = 4
x+y/x-y = 44/20
20x+20y = 44x- 44y
24x = 64y
x/y = 64/24 = 8/3

A boat takes 90 minutes less to travel 36 km downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 kmph, find the speed of the stream?

3/2 = 36/10-x -36/10+x = 36 * 2x/100-x^2
300-3x^2 = 144x
3x^2+144x-300 = 0
x^2+48x-100 = 0
(x+50)(x-2) = 0
Since x can only be positive value, speed of stream = 2 kmph

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