The average speed Alan must travel at for the rest of the journey is 96 km/h.
The given parameters;
- time taken by Alan complete one quarter of the journey = 4 h 15 min = 4.25 h
- average speed of Alan = 64 km/h
- total time of the motion, T = 12 h 45 min = 12.75 h
The first distance traveled by Alan is calculated as;
[tex]d_1 = 64 \ km/h \times 4.25 \ h\\\\d_1 = 272 \ km[/tex]
The total distance traveled by Alan is calculated as;
[tex]\frac{1}{4} \times \ total \ distance = 272 \ km\\\\ total \ distance = 4 \times 272 \ km\\\\ total \ distance = 1,088 \ km[/tex]
The distance traveled by Alan in the second journey is calculated as;
[tex]d_2 = \frac{3}{4} \times 1,088 \ km = 816 \ km[/tex]
The time of motion for the second journey is calculated as;
[tex]t_2 = T- t_1\\\\t_2 = 12.75 \ hr - 4.25 \ hr\\\\t_2 = 8.5 \ hr[/tex]
The average speed of Alan in the second journey is calculated as;
[tex]V = \frac{distance}{time} \\\\V = \frac{816 \ km}{8.5 \ h} = 96 \ km/h[/tex]
Thus, the average speed Alan must travel at for the rest of the journey is 96 km/h.
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