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

Two people simultaneously go from the same place along the same road for a walk to the edge of the loess, located 4 km from the place of departure, one goes at a speed of 2.7 km / h and the other – at a speed of 4.5 km / h, reaching the edge of the loess, the other returns with the same speed back at what distance from the point of departure will they meet?

Let’s find the time it takes for the second one to reach the edge:

4: 4.5 = 40/45 hours.

During this time, the first one will have time to pass:

2.7 * 40/45 = 27/10 * 40/45 = 12/5 km.

Then the distance between them will be:

4 – 12/5 = 8/5 km.

The approach speed will be equal to the sum of their speeds:

2.7 + 4.5 = 6.2 km / h.

Then the meeting will take place through:

12/5: 62/10 = 24/62 hours.

Time before meeting:

40/45 + 24/62 = 356/279 hours.

The distance from the start of the movement will be:

27/10 * 356/279 = 9612/2790 = 3.45 km.

Answer: the required distance is 3.45.

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