A boat takes 8 hours 48 minutes upstream and 4 hours downstream for the same distance. Find the ratio of the boat's speed to the current's speed.

Given data

• Upstream time = 8 h 48 min = 8.8 h
• Downstream time = 4 h

Concept / Approach

• For equal distances, speed ratio = inverse of time ratio.
• Let u be still-water speed, v be current speed. Then (u − v) : (u + v) = (1/8.8) : (1/4) = 4 : 8.8 = 5 : 11.

Step-by-step calculation

Assume u − v = 5k and u + v = 11kAdd: 2u = 16k ⇒ u = 8kSubtract: 2v = 6k ⇒ v = 3kTherefore, u : v = 8 : 3

Verification

Pick k = 1 ⇒ speeds 8 and 3 ⇒ times are proportional to 1/(8 − 3) = 1/5 and 1/(8 + 3) = 1/11; ratio of times = 11:5 which matches 8.8:4 = 2.2:1 ⇒ 11:5 after scaling.

Common pitfalls

• Confusing time ratio with speed ratio; they are reciprocals for equal distances.

Final Answer

8 : 3