A motorboat's speed is 16 km/h in still water. It takes 72 minutes more to go 36 km upstream than to return downstream to the same spot. The speed (in km/h) of the stream is:

Given:

Speed of boat in still water (v_b) = 16 km/h

Distance (d) = 36 km

Time difference (Δt) = 72 minutes = 72/60 hours = 1.2 hours

Formula Used:

Time = Distance / Speed

Speed upstream = v_b - v_s

Speed downstream = v_b + v_s

Calculation:

Time taken upstream (t_up) = d / (v_b - v_s) = 36 / (16 - v_s)

Time taken downstream (t_down) = d / (v_b + v_s) = 36 / (16 + v_s)

t_up - t_down = Δt

⇒ 36 / (16 - v_s) - 36 / (16 + v_s) = 1.2

⇒ 36 [(16 + v_s) - (16 - v_s)] / [(16 - v_s)(16 + v_s)] = 1.2

⇒ 36 [16 + v_s - 16 + v_s] / [16² - v_s²] = 1.2

⇒ 36 [2v_s] / [256 - v_s²] = 1.2

⇒ 72v_s = 1.2 (256 - v_s²)

⇒ 72v_s = 307.2 - 1.2v_s²

⇒ 1.2v_s² + 72v_s - 307.2 = 0

⇒ v_s² + 60v_s - 256 = 0

Using the quadratic formula: v_s = [-b ± √(b² - 4ac)] / 2a

⇒ v_s = [-60 ± √(60² - 4 × 1 × -256)] / 2 × 1

⇒ v_s = [-60 ± √(3600 + 1024)] / 2

⇒ v_s = [-60 ± √4624] / 2

⇒ v_s = [-60 ± 68] / 2

Possible values for v_s:

⇒ v_s1 = (-60 + 68) / 2 = 8 / 2 = 4

⇒ v_s2 = (-60 - 68) / 2 = -128 / 2 = -64

Since the speed of the stream cannot be negative, v_s = 4 km/h.

The speed of the stream is 4 km/h.