Join the growing community of curious minds on IDNLearn.com. Discover prompt and accurate answers from our community of experienced professionals.
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.
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. IDNLearn.com has the answers you need. Thank you for visiting, and we look forward to helping you again soon.