Respuesta :
The average speed is the ratio of the distance covered to the time taken.
- Her average speed for the final 40 miles is approximately 32.66 mph.
Reasons:
Given information;
The distance Hanna travels at 60 miles = 70 miles
The further distance she travels = 40 miles
The average speed of the entire journey = 46 mph
Solution:
The correct response values is arrived at through the following steps
Formula for speed;
[tex]\displaystyle Average \ speed = \mathbf{\frac{Total \ distance }{Time}}[/tex]
Therefore;
[tex]\displaystyle Time= \frac{Total \ distance }{Average \ speed}[/tex]
Plugging in the given values to find the time of travel;
The values of total distance and time are plugged into the above equation to find the time she takes to travel each part of the journey as follows;
The time she takes to travel 70 miles in hours is; [tex]\displaystyle Time= \frac{70}{60} = \frac{7}{6}[/tex]
The time she takes to travel the total distance of 70 miles + 40 miles = 110 miles, is given as follows;
[tex]\displaystyle Time= \frac{70 + 40}{46} = \mathbf{\frac{55}{23}}[/tex]
The time in hours she travels 40 miles is therefore,
[tex]\displaystyle t = \frac{55}{23} -\frac{7}{6} = \frac{169}{138}[/tex]
Calculating her average speed for the final 40 miles;
[tex]\displaystyle Her \ average \ speed \ in \ the \ final \ 40 \ miles = \frac{40 \ miles }{\frac{169}{138} \ hours} \approx \underline{ 32.66 \ mph}[/tex]
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