Two pedestrians set off at once to meet each other from points M and N, the distance between which is 38 km.

Two pedestrians set off at once to meet each other from points M and N, the distance between which is 38 km. After 4 hours the distance between them was reduced to 2 km, and after another 3 hours the first pedestrian had to go to point N by 7 km less than the second to M. find the speed of pedestrians.

Let the speed of one pedestrian be x km / h, and the speed of the second pedestrian – y km / h.

After 4 hours, the distance between them is 2 km, which means that the pedestrians have passed 38 – 2 = 36 km towards each other. We get the equation:

4 * (x + y) = 36.

According to the condition of the problem, in 7 hours one pedestrian will pass 38 – 7 * km, and the second 38 – 7 * y, which is 7 km less. We get the equation:

38 – 7 * x – 7 = 38 – 7 * y,

31 – 7 * x = 38 – 7 * y.

From the first equation we get that x + y = 9, so y = 9 – x.

Substitute this value y into the third equation:

31 – 7 * x = 38 – 7 * (9 – x),

31 – 7 * x = 38 – 63 + 7 * x,

14 * x = 31 – 38 + 63,

14 * x = 56,

x = 4 (km / h) – the speed of one pedestrian.

9 – 4 = 5 (km / h) – speed of the second pedestrian.