J is faster than P. J and P each walk 24 km. Sum of the speeds of J and P is 7…

Time = Distance / Speed. When two quantities have a known sum and a known product (derived from a second constraint), they are the two roots of the quadratic x² − (sum)x + (product) = 0.

1. Let the speed of J be j kmph and the speed of P be p kmph. Given: j + p = 7 kmph.

2. Each walks 24 km, so time taken by J = 24/j hours and time taken by P = 24/p hours. Given: 24/j + 24/p = 14 hours.

3. Combine the fractions on the left: 24(j + p)/(jp) = 14. Substituting j + p = 7: 24 × 7 / (jp) = 14.

4. Solve for the product: jp = 168/14 = 12.

5. So j and p are roots of x² − 7x + 12 = 0, i.e. (x − 3)(x − 4) = 0, giving values 3 and 4.

6. Since J is faster than P (j > p), assign j = 4 kmph and p = 3 kmph.

Check: 24/4 + 24/3 = 6 + 8 = 14 hours, which matches the given total time exactly.

Therefore, J's speed is equal to 4 kmph.