The first step in solving this question is to split the journey into 2 parts. In the first part of the journey, [tex]\frac{2}{3} \times 15 = 10[/tex] miles are covered at a speed of 40 mph. In the second part the journey 5 miles are covered at a speed of 60 mph.
The equation to compute the time of a journey given the speed and distance is [tex]t=\frac{d}{s}[/tex] where [tex]t[/tex] is the time, [tex]s[/tex] is the speed and [tex]d[/tex] is the distance.
The time for the first part of the journey is calculated as shown below,
[tex]t=\frac{d}{t} \\t=\frac{10m}{40mph} =\frac{10}{40} h[/tex].
The time for the second part of the journey is calculated as follows,
[tex]t=\frac{d}{t} \\t=\frac{5m}{60mph} =\frac{5}{60} h[/tex].
The total time is the sum of the times taken to cover each part of the journey and is calculated as shown below,
[tex]t=\frac{10}{40} h+\frac{5}{60} =\frac{30+10}{120} h=\frac{40}{120}h =\frac{1}{3} h[/tex]
The time to cover the journey is a third of an hour or 20 minutes.
