If ying zyiyu covered the first 200 miles of a trip going at 50 mph and the last hundred miles going at 40 mph, what was his average speed for the entire trip? Teacher told me it is not 45

Average speed is (total distance)/(total time).
To find the total time we need to do some division.
Time for 200 miles=200/50=4 hours.
Time for 100=100/40=5/2 hours.
Total time=13/2 hours. Total distance=200+100=300 miles.
Av speed=300/(13/2)=300×2/13=600/13=46.15 mph approx.

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ernikhil ernikhil · Answer 2 · 2021-10-18T13:14:02+02:00

The average speed of ying zyiyu is [tex]46.15\;\rm{mph}[/tex]

Average speed is the ratio of the total distance traveled by a body to the total time taken by the body to cover the total distance.

Here, ying zyiyu covered the first [tex]200\;\rm miles[/tex] of the trip at [tex]50\;\rm mph[/tex] so,

Total time taken by ying zyiyu to cover [tex]200\;\rm miles[/tex] is calculated as-

[tex]t_1=\dfrac{200}{50}\\t_1=4\;\rm hour[/tex]

Similarly, ying zyiyu covered the first [tex]100\;\rm miles[/tex] of the trip at [tex]40\;\rm mph[/tex] so,

Total time taken by ying zyiyu to cover [tex]100\;\rm miles[/tex] is calculated as-

[tex]t_2=\dfrac{100}{40}\\t_2=2.5\;\rm hour[/tex]

So, the total time taken by ying zyiyu to travel [tex]300\;\rm miles[/tex] is [tex]4+2.5=6.5\;\rm hours[/tex]

Now, the average spped is calculated as-

[tex]\rm{Average\;Speed}=\dfrac{Total\;Distance}{Total\;Time}\\\rm{Average\;Speed}=\dfrac{300}{6.5}\\\rm{Average\;Speed}=46.15\;\rm mph[/tex]

Hence, the average speed of ying zyiyu is [tex]46.15\;\rm{mph}[/tex].

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