The speed of a boat in still water is 15 km/h. It can go 15 km upstream and 10 km downstream in a total time of 2 hours. How much time (in hours) will it take to go 32 km downstream?

Given:

Speed of boat in still water = 15 km/h

Upstream distance = 15 km

Downstream distance = 10 km

Total time = 2 hours

Downstream distance to find time = 32 km

Formula used:

Speed = Distance / Time

Upstream speed = Speed of boat - Speed of stream

Downstream speed = Speed of boat + Speed of stream

Calculation:

Let the speed of the stream be x km/h.

Upstream speed = 15 - x km/h

Downstream speed = 15 + x km/h

Time taken for upstream journey:

T_u = 15 / (15 - x)

Time taken for downstream journey:

T_d = 10 / (15 + x)

Total time is 2 hours:

15 / (15 - x) + 10 / (15 + x) = 2

⇒ [15(15 + x) + 10(15 - x)] / [(15 - x)(15 + x)] = 2

⇒ (225 + 15x + 150 - 10x) / (225 - x²) = 2

⇒ 375 + 5x = 2(225 - x²)

⇒ 375 + 5x = 450 - 2x²

⇒ 2x² + 5x - 75 = 0

⇒ 2x² + 15x - 10x - 75 = 0

⇒ x(2x + 15) - 5(2x + 15) = 0

⇒ (2x + 15)(x - 5) = 0

⇒ x = 5 (since x cannot be negative)

Downstream speed = 15 + 5 = 20 km/h

Time taken to go 32 km downstream:

Time = 32 / 20 = 1.6 hours

∴ It will take 1.6 hours to go 32 km downstream.