A boat can go 5 km upstream and 7.5 km downstream in 45 minutes. It can also go 5 km downstream and 2.5 km upstream in 25 minutes. How much time (in minutes) will it take to go 6 km upstream?
A
Correct answer
Explanation
Let upstream speed = u km/min, downstream speed = d km/min. From first trip: 5/u + 7.5/d = 45. From second trip: 2.5/u + 5/d = 25. Solving these equations gives u = 1/6 km/min and d = 1/4 km/min. Time for 6 km upstream = 6/(1/6) = 36 minutes. The key insight is that upstream and downstream speeds differ due to the current.