Two people go from the same place for a walk to the edge of the forest, located 3.5 km from the place of departure.

Two people go from the same place for a walk to the edge of the forest, located 3.5 km from the place of departure. The speed of the first person during the first hour was 2.7 km / h, at the beginning of the second hour, the first person decided to increase the speed to 3 km / h. The second person moved to the edge of the forest at a constant speed of 3.6 km / h. Having reached the edge, the second one returns back at a speed of 4 km / h. At what distance from the point of departure will they meet?

Let’s find out how long it takes for the second pedestrian to reach the edge of the forest, if his speed is 3.6 km / h and the distance is 3.5 km:

3.5: 3.6 = 35/10: 36/10 = 35/36 hours.

Let’s find how far the first pedestrian will travel during this time, if he moved at a speed of 2.7 km / h for the first hour:

2.7 * 35/36 = 27/10 * 35/36 = 3/2 * 7/4 = 21/8 km.

Let’s find how far the first pedestrian will walk before the second hour at a speed of 2.7 km / h:

(1 – 35/36) * 2.7 = 1/36 * 27/10 = 3/40 km.

Let’s find how far the second pedestrian will travel during this time:

1/36 * 4 = 1/9 km.

Let’s find the distance between pedestrians after the first hour:

35/10 – 21/8 – 3/40 – 1/9 = 7/2 – 21/8 – 3/40 – 1/9 = 1260/360 – 945/360 – 27/360 – 40/360 = 248 / 360 = 31/45 km.

Let’s find out how long it takes pedestrians to walk this distance before the meeting:

31/45: (3 + 4) = 31/315 hours.

It remains to find how many km the first pedestrian will pass during this time:

3 * 31/315 = 91/315 km.

Let’s find at what distance from the point of departure the meeting took place:

91/315 + 21/8 + 3/40 = (3640 + 33075 + 945): 12600 = 37660/12660 = 3 km