Respuesta :
Given:
Lucy left the beach and drove back towards home, driving at a rate of 60 mph and Lucy's friend left the beach for home 4 hours later, and drove 75 mph.
To find:
How long it took Lucy's friend to catch up to Lucy.
Solution:
Let Lucy's friend catch up with Lucy in t hours after she starts from the beach.
Since, Lucy started 4 hours before her friend, so she traveled for (t + 4) hours. So, the distance traveled by Lucy is:
[tex]d_1=60(t+4)[/tex]And the distance traveled by Lucy's friend is:
[tex]d_2=75(t)[/tex]Now, the distances traveled by Lucy and her friend till she catches up to Lucy are equal. SO,
[tex]\begin{gathered} d_1=d_2 \\ 60(t+4)=75t \\ 60t+240=75t \\ 15t=240 \\ t=\frac{240}{15} \\ t=16 \end{gathered}[/tex]Thus, it took 16 hours to catch up to Lucy.
