Let t be the number of hours it takes Charlie to catch up with Bernie.
[tex]\begin{gathered} \text{Speed}=\frac{dis\tan ce}{\text{time}} \\ \text{distance}=\text{speed}\times time \end{gathered}[/tex]
Given:
For Charlie
time = t
speed = 20mph
[tex]\begin{gathered} \text{Charlie's distance covered = sp}eed\text{ x time} \\ Charlie^{\prime}sdistance=20\text{ x t } \\ =20t\text{ miles} \end{gathered}[/tex]
For Bernie, he has started 1 hour earlier
Given:
time = t + 1
speed = 15mph
[tex]\begin{gathered} \text{Bernie's distance covered will be;} \\ \text{speed x time = 15(t+1)} \\ =15t+15\text{ miles} \end{gathered}[/tex]
Hence, to get the time it will take for Charlie to catch up, we equate the distance both of them covered
[tex]\begin{gathered} 15t+15=20t \\ \text{Collecting the like terms,} \\ 15=20t-15t \\ 15=5t \\ \text{Dividing both sides by 5,} \\ t=\frac{15}{5} \\ t=3\text{hours} \end{gathered}[/tex]
Therefore, it will take Charlie 3hours to catch up with Bernie.
