Multiple choice

$A$ and $B$ walk from $X$ to $Y$, a distance of $27$ km, at $5$ km/hr and $7$ km/hr, respectively. $B$ reaches $Y$ and immediately turns back meeting $A$ to $Z$. What is the distance from $X$ to $Z $?

  1. $22.5 $ km
  2. $20.0$ km
  3. $25.0 $ km
  4. $24.5 $ km
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A and B travel 27 km. B reaches Y (27 km) and turns back. When they meet at Z, the total distance covered by both is 27 + 27 = 54 km. The time taken is 54 / (5 + 7) = 4.5 hours. The distance from X to Z is the distance A travels in 4.5 hours, which is 5 * 4.5 = 22.5 km.

AI explanation

When B meets A, they have together covered double the distance between X and Y, which is 54 km. Their combined relative speed is 5 km/hr plus 7 km/hr, equaling 12 km/hr. The total time taken until they meet is 54 km divided by 12 km/hr, which equals 4.5 hours. In that time, A has walked from X towards Y at 5 km/hr, covering a distance of 5 times 4.5, which is 22.5 km.

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