The pedestrian first climbed the mountain at a speed of 2 km / h and then descended at a speed of 4 km / h.

The pedestrian first climbed the mountain at a speed of 2 km / h and then descended at a speed of 4 km / h. Find the common path traveled by a pedestrian if the descent was 2 km longer than the ascent, and the time taken for the entire journey was 5 hours.

x km – ascent
(x + 2) km – downhill
Rise time – x / 2
Descent time – (x + 2) / 4
x / 2 + (x + 2) / 4 = 5
* (bring to a common denominator by multiplying x / 2 by 2)
2x / 4 + (x + 2) / 4 = 5
* (Get rid of the denominators by multiplying both sides of the equation by 4)
2x + x + 2 = 20
3x + 2 = 20
3x = 18
x = 6 km – ascent
6 +2 = 8 km – descent
6 + 8 = 14 km
Answer: the entire distance traveled is 14 km