Multiple choice

A motor boat whose speed is $18$ km/h in still water takes $1$hour more to go $24$ km upstream than to return downstream to the same spot. The speed of the stream is

  1. $6$ km/hr
  2. $5$ km/hr
  3. $3.5$ km/hr
  4. $4.5$ km/hr
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let v be the stream speed. Upstream speed is 18-v, downstream is 18+v. Time difference is 24/(18-v) - 24/(18+v) = 1. Solving 24(18+v - 18+v) / (324 - v^2) = 1 gives 48v = 324 - v^2, or v^2 + 48v - 324 = 0. Factoring (v+54)(v-6) = 0 gives v = 6.

AI explanation

Let the speed of the stream be v, making the upstream speed 18 - v and the downstream speed 18 + v. The equation from the given time difference is 24 / (18 - v) = 24 / (18 + v) + 1. Multiplying by (18 - v)(18 + v) gives 24(18 + v) = 24(18 - v) + (324 - v^2), which simplifies to 48v = 324 - v^2, or v^2 + 48v - 324 = 0. Solving this quadratic equation yields v = 6. The result is 6 km/hr.

Keep practicing — related questions