Multiple choice

Places $A$ and $B$ are $100 km$ apart from each other on a highway. A car starts from A and another from B at the same time. If they move in the same direction, they meet in $10$ hours and if they move in opposite directions they meet in $1$ hour $40$ minutes. Find the speed of the cars from places A and B, respectively.

  1. $45 km/hr, 25 km/hr$
  2. $65 km/hr, 75 km/hr$
  3. $35 km/hr, 25 km/hr$
  4. $60 km/hr, 45 km/hr$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speeds be u and v. Same direction: 100/(u-v) = 10 => u-v = 10. Opposite direction: 100/(u+v) = 5/3 => u+v = 60. Adding equations: 2u = 70 => u = 35. Then v = 25.

AI explanation

When moving in opposite directions, their relative speed is 100 km divided by 1 hour 40 minutes (or 5/3 hours), which equals 60 km/hr. When moving in the same direction, their relative speed is 100 km divided by 10 hours, which equals 10 km/hr. Solving the equations a + b = 60 and a - b = 10 yields speeds of 35 km/hr and 25 km/hr. The result is 35 km/hr, 25 km/hr.

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