A boat takes a total of 6 hours to travel 45 km downstream

Solution

Let the upstream and downstream speed of boat be 'U' km/h and 'D' km/h respectively.
So, (45/D) + (30/U) = 6 --------- (I)
And, (30/D) + (60/U) = 8 -------- (II)
On solving 2 X equation I - equation II,
We get, 2 X [(45/D) + (30/U) ] - [(30/D) + (60/U) ] = 2 X 6 - 8
Or, (90/D) + (60/U) - (30/D) - (60/U) = 12 - 8
Or, (60/D) = 4
Or, 'D' = 15
On putting value of 'D' in equation I,
We get, (45/15) + (30/U) = 6
Or, 3 + (30/U) = 6
Or, (30/U) = 3
Or, 'U' = 10
Speed of stream = (1/2) X (downstream speed - upstream speed)
= (1/2) x (15 - 10) = 2.5 km/h