From point A to point B, a cyclist left at a speed of 12 km / h. An hour later, a second cyclist left B to A to meet

| August 9, 2021 | education

From point A to point B, a cyclist left at a speed of 12 km / h. An hour later, a second cyclist left B to A to meet him at a speed of 14 km / h and met the first one a second hour after his departure. a) What is the distance from A to B? b) How long did the first cyclist take for the entire journey?

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

2. Speed ​​of the first cyclist: V1 = 12 km / h;

3. Speed ​​of the second cyclist: V2 = 14 km / h;

4. The second cyclist left later at: To = 1 hour;

5. The meeting took place after his departure in: Tb = 0.5 hour;

6. The total speed of cyclists: Vc = V1 + V2 = 12 + 14 = 26 km / h;

7. Let’s calculate the distance between points:

Tb = (S – So) / Vc = (S – V1 * To) / Vc;

S = Vc * Tb + V1 * To = 26 * 0.5 + 12 * 1 = 25 km;

8. Time of the first cyclist on the way from point A to point B:

T1 = S / V1 = 25/12 = (24/12) + 1/12 = 2 hours 5 minutes.

Answer: the distance between points is 25 km, the time for the first cyclist to travel to point B is 2 hours 5 minutes.



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