Answer:
41.67 [tex]\frac{km}{h}[/tex]
Step-by-step explanation:
First, let's find the length of the entire journey. Since the remaining distance, after completing [tex]\frac{3}{5}[/tex] of the journey, was 200 km, we will use this to find the length of the entire journey. I'll use the variable [tex]j[/tex] for the length of the journey:
[tex]\frac{3}{5}j=200km\\3j=5(200km)\\j=\frac{5}{3}(200km)\\[/tex]
[tex]j=\frac{1000}{3}[/tex] ≈ 333.33 km
Now, to find the average speed for his whole journey we use the following formula:
[tex]\frac{total Distance}{totalTime}[/tex]
The total time is simply 5 + 3 or 8 hours, and we already found the total distance to be about 333.33 kilometres. Now we can plug these values into the equation:
[tex]\frac{333.33km}{8hours}[/tex] ≈ 41.67 [tex]\frac{km}{h}[/tex]
If you wanted to find the speed of the first portion of his trip, you could do as follows to find the distance of the first portion and then plug that into the above equation for average speed:
The original [tex]\frac{2}{5}[/tex] of the journey, or [tex]\frac{2}{5}j[/tex], would have been:
[tex]\frac{2}{5}j\\\\\frac{2}{5}(\frac{1000}{3})\\[/tex]
[tex]\frac{400}{3}[/tex] ≈ 133.33 km
