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In 4\(\frac{1}{2}\) hours, Jack can cover a distance of 6 km more than the distance covered by Jill in 3 hours. In 6 hours, Jack can cover 5 km less than the distance covered by Jill in 5 hours. What is the average speed of Jack in km/hr?
1. 10
2. 9
3. 11
4. 12

1 Answer

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Correct Answer - Option 1 : 10

GIven:

In 4\(\frac{1}{2}\) hours, Jack can cover a distance of 6 km more than the distance covered by Jill in 3 hours

In 6 hours, Jack can cover 5 km less than the distance covered by Jill in 5 hours

Concept used:

linear equations in two variables

Calculation:

Let the speed of Jack be x km/h and Jill be y km/h

9x/2 - 3y = 6      ----(i) × 4

⇒ 18x - 12y = 24      ----(iii)

5y - 6x = 5      ----(ii) × 3

⇒ 15y - 18x = 15      ----(iv)

By (iii) + (iv) we get

3y = 39

⇒ y = 13

9x/2 = 6 + 3 × 13

⇒ 9x = 45 × 2

⇒ x = 10

∴ Average speed of Jack is 10 km/h

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