Multiple choice

One day, Manisha covered a distance of $24$ km at $x$ km/hr and another $40$ km at $y$ km/hr. Next day, she covered $18$ km at $x$ km/hr and another $48$ km at $y$ km/hr. If each day she took $9$ hours to complete her journey find the values of $x$ and $y$.

  1. $x = 7$ and $y = 12$
  2. $x = 6$ and $y = 8$
  3. $x = 2$ and $y = 5$
  4. $x = 17$ and $y = 3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Day 1: 24/x + 40/y = 9. Day 2: 18/x + 48/y = 9. Multiply first by 3 and second by 4: 72/x + 120/y = 27 and 72/x + 192/y = 36. Subtracting: 72/y = 9 => y = 8. Substitute y=8 into first: 24/x + 40/8 = 9 => 24/x + 5 = 9 => 24/x = 4 => x = 6.

AI explanation

We form a system of linear equations based on the Time equals Distance divided by Speed formula: (24 divided by x) + (40 divided by y) = 9 and (18 divided by x) + (48 divided by y) = 9. To check option B, we substitute x = 6 and y = 8 into the first equation to get (24 divided by 6) + (40 divided by 8), which equals 4 + 5 = 9 hours. Verifying with the second equation gives (18 divided by 6) + (48 divided by 8), which equals 3 + 6 = 9 hours, confirming the values are x = 6 and y = 8.

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