Given:

Timothy climbed a mountain in two days. Timothy spent a total of 14 hours climbing the mountain.  

On the second day, Timothy walked at an average SPEED that was half a kilometer per hour faster, but was two hours less than what Timothy walked on the first day.  

To find:

If the total DISTANCE Timothy COVERED during the two days, was 52 km, how many kms per hour did Timothy walk on the second day?​

Solution:

Timothy spent a total of 14 hours climbing the mountain. On the second day, Timothy walked two hours less than what Timothy walked on the first day.

Let time TRAVELLED during first day = x

Let time travelled during the second day = x - 2

Total time = 14

x + (x - 2) = 14

x = 8 hours

Therefore, Timothy walked 8 hours on the first day and (8 - 2) = 6 hours on the second day.

The total distance Timothy covered during the two days, was 52 km

we use the formula, speed = distance/time

speed × time = distance

On the second day, Timothy walked at an average speed that was half a kilometre per hour faster

s × 8 + (s + 0.5) (6) = 52

s × 8 + (s + 1/2) (6) = 52

8s + 6s + 3 = 52

14s = 49

s = 49/14 = 3.5

s = 3.5 km/hr

Thus the speed on the first day = 3.5 km/hr

Thus the speed on the second day = 3.5 + 0.5 = 4 km/hr

Therefore, Timothy walked 4 km/hr on the second day.