Multiple choice

A boat travels in a stream from point A to point B and then back to A taking a total of 4.5 hours. Another boat travels from A to B in 6 hours and from B to A in 2 hours. Find the total time, in hours, taken by the faster boat to travel from A to B.

  1. 2

  2. 2.5

  3. 1

  4. 1.5

Reveal answer Fill a bubble to check yourself
D Correct answer
AI explanation

Let the distance between point A and point B be D. The second boat travels from A to B in 6 hours and from B to A in 2 hours, so its downstream speed is D/6 and its upstream speed is D/2. By the boat and stream formulas, the stream speed is half the difference of these speeds, calculated as (D/2 - D/6) divided by 2, which equals D/6. The first boat takes a total of 4.5 hours for the round trip, giving the equation D divided by the downstream speed plus D divided by the upstream speed equals 4.5. Substituting the stream speed D/6 into the first boat's speeds gives its downstream speed as its still water speed plus D/6 and its upstream speed as its still water speed minus D/6, and solving the time equation yields its still water speed as 5D/6. Therefore, the first boat's downstream speed is 5D/6 plus D/6, which equals D, meaning it takes 1 hour to travel from A to B.