Question

A boat goes 60 km and back to
starting point in 10 hours. The time
taken by the boat to row 3 km
downstream is equal to the time
o taken by the boat to row 2 km
upstream. Find the speed of boat
in still water and the rate of current​

Answer 1

Step-by-step explanation:

let the speed of boat in still water be x

speed of current= y

so upstream speed = x-y

downstream speed = x+y

now

t1 = time taken by boat to go 60 km upstream

t1 = 60/ ( x-y) [ time = distance / speed )

t2 = time taken by boat to go 60 km downstream

t 2= 60/(x+y)

according to question

t1 + t2 = 10

60/(x-y) + 60 / ( x+y) = 10 ..........EQ 1

now

t3 = time taken by boat to go 2 km upstream

t3 = 2/ ( x-y)

t4 = time taken by boat to go 3 km downstream

t4 = 3/ ( x+y)

according to question

t3 = t4

so

2/ ( x-y) = 3/ (x+y) ............EQ 2

put in EQ 1 and 2

1/(x-y )= A

1/(x+y )= B

we get

60 A + 60 B = 10 ...........EQ 3

2A = 3B ..........EQ 4

A = 3B /2

60 A = 90 B

put in EQ 3 we get

90 B + 30 B = 10

120 B = 10

B = 1/12

x+y = 12 ...........EQ 5

put the value of B in EQ 4 we get

A= 1/8

so x-y = 8

x = 8+y

put in EQ 5

y = 2

x = 10

so speed of current = 2 km/ hour

speed of boat in still water = 10 km / hour