Question

Matthew drives 54 miles per hour. Benjamin drives 47 miles per hour. They started at the same spot, and drove in opposite directions. Aftersome time, they were 1272.6 miles apart. How much time has passed?After _____ hours, Matthew and Benjamin were 1272.6 miles apart.

Answer 1

Matthew and Benjamin start from the same spot and drives in opposite directions.

Given:

`\begin{gathered} \text{Matthew's sp}eed=54mph \\ \text{Benjamin's sp}eed=47mph \\ \text{Distance apart after time (t)=1272.6miles} \end{gathered}`

The formula for speed is given by;

`\begin{gathered} \text{Speed}=\frac{dis\tan ce}{\text{time}} \\ \text{Hence, } \\ \text{distance}=\text{speed}* time \end{gathered}`

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;

`\begin{gathered} \text{distance}=\text{speed}* time \\ m=54* t \\ m=54t \end{gathered}`

Benjamin's distance is calculated below;

`\begin{gathered} \text{distance}=\text{speed}* time \\ b=47* t \\ b=47t \end{gathered}`

The distance covered by the two of them in opposite directions is their distance apart from the starting point.

Hence,

`m+b=1272.6`
`\begin{gathered} 57t+47t=1272.6 \\ 101t=1272.6 \\ \text{Dividing both sides by 101 to get the time t,} \\ t=(1272.6)/(101) \\ t=12.6\text{hrs} \end{gathered}`

Therefore, after 12.6hours, Matthew and Benjamin were 1272.6 miles apart.