Multiple choice

A motot boat covers the distance between two spots on the river banks in $t_1=8h$ and $t_2=12h$ in down stream and upstream respectively. The time required for the boat to cover this distance in still water will be:

  1. $6.9$ hr
  2. $9.6$ hr
  3. $69$ second
  4. $96$ second
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the still-water speed be u and the stream speed be v. The downstream and upstream speeds are D/8 and D/12, so 2u = D/8 + D/12 = 5D/24. Therefore, the still-water travel time is D/u = 48/5 = 9.6 hours.

AI explanation

Let the distance between the two spots be D, the speed of the boat in still water be u, and the speed of the stream be v. Using the basic speed formula for downstream and upstream, D equals 8 times u plus v and D equals 12 times u minus v. Equating the two expressions for D gives 8u plus 8v equals 12u minus 12v, which simplifies to 20v equals 4u, or u equals 5v; substituting this into the downstream equation yields D equal to 48v. The time required to cover this distance in still water is D divided by u, which becomes 48v divided by 5v, resulting in a time of 9.6 hours.

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