Question

rani can row her boat at a speed of 5 km/h in still water . if it takes her 1 hr more to row the boat 5.25 km upstream than to return downstream , then find the speed of the stream

Answer 1

Upstream DATA:
rate = 5 - s ; distance = 5.25 km ; time = d/r = 5.25/(5-s) hrs.
--------------------
Downstream DATA:
rate = 5+s ; distance = 5.25 km ; time = d/r = 5.25/(5+s) hrs
--------------------
Equation:
time - time = 1 hr
5.25/(5-s) - 5.25/(5+s) = 1
-----
5.25*5 + 5.25s - 5.25*5 + 5.25s = 25-s^2
--------
10.5s = 25-s^2
--------
s^2 + 10.5s - 25 = 0
-----
Factor:
(s-2)(s+12.5) = 0
------
Positive solution:
s = 2 km/hr (speed of the stream)
=====================
Cheers,
Stan H.
=====================

Answer 2

et the speed of the stream be x km/h

Speed of boat upstream =(5-x) km/h

speed of boat downstream = (5+x) km/h

Distance travelled by boat in upstream=Distance travelled by boat in downstream=5.25 Km.

ATQ:-

→ 5.25(1/(5-x)-1/(5+x)=1.

→ 5.25 (2x/(25-x^2)=1.

→ 10.5x=25-x^2=0.

→ (x^2+10.5x-25=0.

→ (x+12.5)(x-2)=0.

→ x=2 Or x= -12.5

Speed can't be negative. So speed = 2 km/h