Question

Два че­ло­ве­ка од­но­вре­мен­но от­прав­ля­ют­ся из од­но­го и того же места по одной до­ро­ге на про­гул­ку до опуш­ки леса, на­хо­дя­щей­ся в 4 км от места от­прав­ле­ния. Один идёт со ско­ро­стью 2,7 км/ч, а дру­гой — со ско­ро­стью 4,5 км/ч. Дойдя до опуш­ки, вто­рой с той же ско­ро­стью воз­вра­ща­ет­ся об­рат­но. На каком рас­сто­я­нии от точки от­прав­ле­ния про­изойдёт их встре­ча?

Answer 1

Решение на изображении

Answer 2

Problem Setup

Two individuals are simultaneously departing from the same location for a walk to the edge of a forest, which is 4 km away. One person walks at a speed of 2.7 km/h, while the other walks at a speed of 4.5 km/h. After reaching the edge of the forest, the second person returns at the same speed.

Calculating the Meeting Point

To find the meeting point, we can calculate the time it takes for each person to reach the forest's edge and then use that time to determine where they will meet.

The time it takes for the first person to reach the forest's edge can be calculated using the formula: $$ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{4 \text{ km}}{2.7 \text{ km/h}} = 1.48 \text{ hours} $$

The time it takes for the second person to reach the forest's edge can be calculated using the same formula: $$ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{4 \text{ km}}{4.5 \text{ km/h}} = 0.89 \text{ hours} $$

After reaching the edge of the forest, the second person returns at the same speed, so the total time for the second person to meet the first person is twice the time it took to reach the edge of the forest: $$ \text{Total Time for Second Person} = 2 \times 0.89 \text{ hours} = 1.78 \text{ hours} $$

Now, we can calculate the distance the first person travels during the time it takes for the second person to meet them: $$ \text{Distance} = \text{Speed} \times \text{Time} = 2.7 \text{ km/h} \times 1.78 \text{ hours} = 4.806 \text{ km} $$

Answer

The two individuals will meet approximately 4.806 km from the starting point.