Question

A man can row 5 km upstream and 3 km downstream in 35 hours also he can row 2 km upstream and 44 km downstream in 28 hours find the speed of man in still water

Answer 1

■let the speed of boat upstream =(x_y)km/h
also ,time=distance/speed
in 1st case when boat goes 30km upstream, let the time taken ,in hour,be
■ t;d/s =5/x-y
■ let t2 be time in hours,taken by the boat to go 3km downstream,
t2=d/s, 3/x+y
■ Total Time taken t1+t2 is,35 hours .therefore we get equation:::
5/(x-y)+3/(x+y)=35
■ N 2ND CASE,in 28 hours it can go 2km upstream and 44 km downstream, WE GET EQUATION AS,,,,
2/(x-y) +44/(x+y)=28
■ put,1/(x-y)=U
■and ,1/(x+y)=v
■ ON SUBSTITUTING THESE VALUES IN EQUATIONS (1 ) AND (2) WE GET A PAIR OF LINEAR EQUATIONS...

■5U+3V=35 ...OR 5U+3V _35 =0
■2U+44V=28...OR 2U+44V-28=0
it's getting too lengthy....HOPE u r able to solve these equations and get the required values of x and y..
Anyways it's the correct procedure, so once u understand the procedure u will b able to solve any type of equation..
Enjoy maths ..

Answer 2

let,the speed of the man in still water be x km /hr

let ,the speed of the stream be y km /hr

then , the speed of boat downstream is (x+y)km/hr

and the speed of boat upstream is (x-y )km/hr

time= distance /speed

case 1

1. 5km upstream in t1 hrs

2. 3km downstream in t2 hrs

t1 = 5/ x-y

t2=3/ x+y

t1+t2= 35 hrs (given)

5/x-y + 3/x+y = 35 --------------(1)

case 2

1. 2km upstream in t3 hrs

2. 44km downstream in t4 hrs

t3= 2/x-y

t4=44/x+y

t3+t4=28 (given)

2/x-y + 44/x+y = 28 --------------(2)

now,let 1/x-y= u

and, 1/x+y= v

then....

5u +3y=35 ----------------(3)

2u+44v=28 ----------------(4)

now solve these equations