Trimothy climbed the mountain in two days. Trimothy spent a total of 14 hours climbing the mountain. On the second day, Trimothy walked at an average speed that was half a kilometre per hour faster, but was two hours less than what Timothy walked on the first day. If the total distance Timothy covered during the two days was 52 kilometres. How many kilometres per hour did Timothy walk on the second day?

The speed in kilometers per hour with which Timothy walked on the second day is 4 km/h    

Step-by-step explanation:

The time period in which Timothy climbed the mountain = 2 days

The total time Timothy spent in climbing the mountain = 14 hours

The average speed with which Timothy walked on the second day = 0.5 km/h faster than he walked the first day

The time duration Timothy walked on the second day =2 hours less than he walked on the first day

The total distance Timothy covered in the two days = 52 kilometers

Let x represent the speed in kilometers per hour with which Timothy walked on the first day and let y represent the speed in kilometers per hour with which Timothy walked on the second day

Also, let t represent the number of hours Timothy walked on the first day

Therefore, we have;

x + 0.5 = y...(1)

x × t + y × (t - 2) = 52...(2)

t + t - 2 = 14...(3)

From equation (3), we have;

t + t - 2 = 14

2·t = 14 + 2 = 16

t = 16/2 = 8

The number of hours Timothy worked on the first day, t = 8 hours, and the number of hours Timothy walked on the second day is t - 2 hours = 8 hours - 2 hours = 6 hours

From equation (1) and (2), we have;

x × t + y × (t - 2) = 52

y = x + 0.5

Which gives;

x × t + y × (t - 2) = x × t + (x + 0.5) × (t - 2) =  x × 8 + (x + 0.5) × (8 - 2) = 52

x × 8 + (x + 0.5) × (8 - 2) = x × 8 + (x + 0.5) × 6 = x × 8 + 6 × x + 3 = 52

14·x + 3 = 52

x = (52 - 3)/14 = 3.5

The speed in kilometers per hour with which Timothy walked on the first day = x = 3.5 km/h

From equation (2), we have;

y = x + 0.5 = 3.5 + 0.5 = 4

y = 4

The speed in kilometers per hour with which Timothy walked on the second day = y = 4 km/h.

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step-by-step explanation: