Answer:
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.
