Two people simultaneously go from the same place along the same road for a walk to the edge of the forest

Two people simultaneously go from the same place along the same road for a walk to the edge of the forest, located 4 km from the place of departure, one going at a speed of 2.7 km / h, and the other at a speed of 4.5 km / h. Having reached the edge, the second one returns back at the same speed. At what distance from the point of departure will they meet?

The solution of the problem:

1. Distance to the edge: S = 4 km;

2. Speed ​​of the first tourist: V1 = 2.7 = (27/10) km;

3. Speed ​​of the second tourist: V2 = 4.5 = (9/2) km;

4. Time, during which the second tourist reached the edge:

T = S / V2 = 4 / (9/2) = (8/9) hour;

5. Distance covered by the first tourist in time T:

S1 = V1 * T = (27/10) * (8/9) = (12/5) km;

6. The distance they need to walk before the meeting:

S0 = S – S1 = 4 – (12/5) = (8/5) km;

7. Time before meeting:

T0 = ​​S0 / (V1 + V2) = (8/5) / ((27/10) + (9/2)) = (2/9) hour;

8. Distance covered by the first tourist during T0:

S3 = V1 * T0 = (27/10) * (2/9) = (3/5) km;

9. Distance from the starting point to the meeting point Sv:

Sw = S1 + S3 = (12/5) + (3/5) = 3 km.

Answer: the meeting of tourists will take place at a distance of 3 km from the point of departure.