A passenger left point A to point B. After 3/4 hours a cyclist followed him. When the cyclist arrived at point B

A passenger left point A to point B. After 3/4 hours a cyclist followed him. When the cyclist arrived at point B, the pedestrian had 3/8 of the way to go. How many hours will a pedestrian spend on the entire journey if the cyclist catches up with a passenger in the middle of the journey?

1. The distance between points A and B is equal to: S km;

2. The speed of the pedestrian is equal to: Vn km / h;

3. Cyclist speed: Vb km / h;

4. Differential removal speed: Vp = (Vb – Vn) km / h;

5. The cyclist left after the pedestrian for: To = 3/4 hours;

6. During this time the pedestrian covered the distance: So km;

So = Vn * To;

7. Time for which the cyclist will catch up with the pedestrian: Tb hour;

Tb = So / Vp = (Vn * To) / (Vb – Vn);

8. The cyclist will spend the same time on the second half of the journey:

Tb = (S / 2) / Vb;

S / 2 = Vb * Tb;

9. During this time, a pedestrian will pass:

Sn = Vn * Tb

10. Difference: S / 2 – Sn = Sk = (3/8 * S) km;

Sk = Vb * Tb – Vn * Tb = Tb * (Vb – Vn) =

((Vn * To) / (Vb – Vn)) / (Vb – Vn) = Vn * To = So;

11. Distance So the pedestrian has passed To:

Vn = So / To = Sk / To = (3/8 * S) / (3/4) = (S / 2) km / h;

12. A pedestrian will cover the whole way in: Tn hour;

Tn = S / Vn = S / (S / 2) = 2 hours;

13. This solution is mathematical. The logical solution is this: half way the pedestrian’s handicap To = 3/4 hours. In the second half of the way, he lagged behind by Sk = 3/8 * S km. Thus, for To, he passed So = Sk km;

Tn = To * (S / Sk) = 3/4 * (S / (3/8 * S) = (3/4) / (3/8) = 2 hours.

Answer: a pedestrian will spend 2 hours for the entire journey.