The time taken by a boat to go 18 km downstream is equal to the time taken by it to go 10.8 km upstream. The speed of the boat in still water is 8 km/h. How much time (in hours) will the boat take to go 45 km upstream ?

Given:

Distance downstream (D_down) = 18 km

Distance upstream (D_up) = 10.8 km

Time taken downstream (T_down) = Time taken upstream (T_up)

Speed of the boat in still water (V_b) = 8 km/h

Formula used:

Speed = Distance / Time ⇒ Time = Distance / Speed

Speed downstream (V_down) = V_b + V_c (where V_c is the speed of the current)

Speed upstream (V_up) = V_b - V_c

Calculation:

From the given condition, T_down = T_up

⇒ D_down / V_down = D_up / V_up

⇒ 18 / (V_b + V_c) = 10.8 / (V_b - V_c)

⇒ 18 / (8 + V_c) = 10.8 / (8 - V_c)

⇒ 18 × (8 - V_c) = 10.8 × (8 + V_c)

⇒ 144 - 18V_c = 86.4 + 10.8V_c

⇒ 144 - 86.4 = 10.8V_c + 18V_c

⇒ 57.6 = 28.8V_c

⇒ V_c = 57.6 / 28.8

⇒ V_c = 2 km/h

V_up = V_b - V_c

⇒ V_up = 8 - 2

⇒ V_up = 6 km/h

Time taken to go 45 km upstream:

Time = Distance / Speed = 45 / 6

⇒ Time = 7.5 hours

∴ The correct answer is option 2.