Multiple choice

At his usual rowing rate, Rahul can travel $12$ miles downstream in a certain river in $6$ hours less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for his $24$ -mile round trip, the downstream $12$ miles would then take only one hour less than the upstream $12$ miles. What is the speed of the current in miles per hour?

  1. $1 \dfrac { 1 } { 3 }$
  2. $1 \dfrac { 2 } { 3 }$
  3. $2 \dfrac { 1 } { 3 }$
  4. $2 \dfrac { 2 } { 3 }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let v be rowing speed and c be current speed. 12/(v-c) - 12/(v+c) = 6. Also, 12/(2v-c) - 12/(2v+c) = 1. Solving these equations for c yields 8/3 or 2 2/3.

AI explanation

Let Rahul's rowing speed in still water be u and the speed of the current be c. Using the condition that the downstream journey takes 6 hours less than upstream, the equation 12/(u-c) - 12/(u+c) = 6 simplifies to u squared minus c squared equals 4c. The second condition states that doubling the rowing speed makes the time difference 1 hour, so 12/(2u-c) - 12/(2u+c) = 1, which simplifies to 4(u squared) minus c squared equals 4c. Subtracting the first simplified equation from the second gives 3(u squared) equals 12, meaning u equals 2. Placing u equals 2 back into the first equation gives 4 minus c squared equals 4c, or c squared plus 4c minus 4 equals 0. Solving this quadratic equation yields a positive current speed of 2 2/3 miles per hour.

Keep practicing — related questions