A boat covers 12 km upstream and 18 km downstream covers the distance 3 h, while it covers 36 km upstream and 24 km downstream covers the distance \(6{{1} \over 2}\) hr. What is the speed of the current.

A boat covers 12 km upstream and 18 km downstream covers the distance 3 h, while it covers 36 km upstream and 24 km downstream covers the distance \(6{{1} \over 2}\) hr. What is the speed of the current. Correct Answer 2 km/h

Given:

Boat cover distance in upstream = 12 km 

Boat Cover distance in downstream = 18 km

Total time = 3 hr

Boat cover distance in upstream = 36 km 

Boat Cover distance in downstream = 24 km

Total time = 6 (1/2) hr

Formula Used:

(Distance)_upstream/(Speed of boat - speed of river) + (Distance)_downstream /(speed of boat + speed of river) = Total time

Calculation:

Let speed of boat be X and speed of river be Y

According to question,

⇒ 12/(X - Y) + 18/(X + Y) = 3     ----(1)

⇒ 36/(X - Y) + 24/(X + Y) = 13/2      ----(2)

By equation (1)  × 3 - equation (2)

⇒ 54/(X + Y) - 24/(X + Y) = 9 - 13/2

⇒ 30/(X + Y) = 5/2

⇒ X + Y  = 12      ----(3)

From equation (1)

⇒ 12/(X - Y) + 18/12 = 3

⇒ 12/(X - Y) = 3 - 3/2

⇒ X - Y = (12 × 2)/3

⇒ X - Y = 8      ----(4)

Solve equation (3) and (4)

⇒ 2y = 4

⇒ y =2

∴ Speed of current is 2 km/h.