Data:
Distance recorred by Mozelle Williams:W
Distance recorred by Melvin Kast: K
W and K start toward each other from 150 miles apart
[tex]W+K=150[/tex]Distance:
[tex]\begin{gathered} \text{speed}=\text{distance}/\text{time} \\ \\ \text{distance}=\text{speed}\cdot\text{time} \end{gathered}[/tex]Mozelle leaves 1 hour before Melvin. Mozelle travels at 30 mph, Melvin at 20 mph:
If t is the time traveled by Mozelle
[tex]\begin{gathered} M=30\text{mph}\cdot t \\ K=20\text{mph}\cdot(t-1) \end{gathered}[/tex]As the sum of distances is 150 miles:
[tex]30t+20(t-1)=150[/tex]Use the equation above to find t (time traveled)
[tex]\begin{gathered} 30t+20t-20=150 \\ 50t-20=150 \\ 50t=150+20 \\ 50t=170 \\ \\ t=\frac{170}{50} \\ \\ t=3.4h \end{gathered}[/tex]Then, Melvin traveled for a time of:
[tex]t-1=3.4h-1=2.4h[/tex]At a speed of 20 mph the distance traveled in 2.4h is:
[tex]\text{distance}=20\text{mph}\cdot2.4h=48m[/tex]Then, Miles have traveled 48 miles when they meet
