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Sagot :
Solution:
Matthew and Benjamin start from the same spot and drives in opposite directions.
Given:
[tex]\begin{gathered} \text{Matthew's sp}eed=54mph \\ \text{Benjamin's sp}eed=47mph \\ \text{Distance apart after time (t)=1272.6miles} \end{gathered}[/tex]The formula for speed is given by;
[tex]\begin{gathered} \text{Speed}=\frac{dis\tan ce}{\text{time}} \\ \text{Hence, } \\ \text{distance}=\text{speed}\times time \end{gathered}[/tex]During the journey, they used the same time but moved at different speeds, hence, they will have different distances.
Let the time both used be represented by t
Let Matthew's distance be represented by m
Let Benjamin's distance be represented by b
Thus,
Matthew's distance is calculated below;
[tex]\begin{gathered} \text{distance}=\text{speed}\times time \\ m=54\times t \\ m=54t \end{gathered}[/tex]Benjamin's distance is calculated below;
[tex]\begin{gathered} \text{distance}=\text{speed}\times time \\ b=47\times t \\ b=47t \end{gathered}[/tex]The distance covered by the two of them in opposite directions is their distance apart from the starting point.
Hence,
[tex]m+b=1272.6[/tex][tex]\begin{gathered} 57t+47t=1272.6 \\ 101t=1272.6 \\ \text{Dividing both sides by 101 to get the time t,} \\ t=\frac{1272.6}{101} \\ t=12.6\text{hrs} \end{gathered}[/tex]Therefore, after 12.6hours, Matthew and Benjamin were 1272.6 miles apart.
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