Multiple choice

A boat can cover 20 km upstream and 32 km downstream together in 3 hours. Also it can cover 40 km upstream and 48 km downstream together in 5.5 hours. What is the speed of the current (in km/h)?

  1. 13

  2. 8

  3. 7

  4. 11

  5. 16

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let boat speed in still water be 'b' km/h and current speed be 'c' km/h. Upstream speed = b - c, downstream speed = b + c. From first condition: 20/(b-c) + 32/(b+c) = 3 hours. From second condition: 40/(b-c) + 48/(b+c) = 5.5 hours. Let x = 1/(b-c) and y = 1/(b+c). Then: 20x + 32y = 3 and 40x + 48y = 5.5. Solving: Multiply first equation by 2: 40x + 64y = 6. Subtract from second: (40x + 48y) - (40x + 64y) = 5.5 - 6, giving -16y = -0.5, so y = 0.5/16 = 1/32. Then b + c = 32. Substituting in first equation: 20x + 32(1/32) = 3, so 20x + 1 = 3, x = 2/20 = 1/10, so b - c = 10. Solving: (b+c) - (b-c) = 32 - 10 = 22, so 2c = 22, c = 11 km/h.