Question

5. Mozelle Williams and Melvin Kast start toward each other from 150 miles apart.Mozelle leaves 1 hour before Melvin. Mozelle travels at 30 mph, Melvin at 20 mph.How many miles will Melvin have traveled when they meet?Answer

Answer 1

Data:

Distance recorred by Mozelle Williams:W

Distance recorred by Melvin Kast: K

W and K start toward each other from 150 miles apart

`W+K=150`

Distance:

`\begin{gathered} \text{speed}=\text{distance}/\text{time} \\ \\ \text{distance}=\text{speed}\cdot\text{time} \end{gathered}`

Mozelle leaves 1 hour before Melvin. Mozelle travels at 30 mph, Melvin at 20 mph:

If t is the time traveled by Mozelle

`\begin{gathered} M=30\text{mph}\cdot t \\ K=20\text{mph}\cdot(t-1) \end{gathered}`

As the sum of distances is 150 miles:

`30t+20(t-1)=150`

Use the equation above to find t (time traveled)

`\begin{gathered} 30t+20t-20=150 \\ 50t-20=150 \\ 50t=150+20 \\ 50t=170 \\ \\ t=(170)/(50) \\ \\ t=3.4h \end{gathered}`

Then, Melvin traveled for a time of:

`t-1=3.4h-1=2.4h`

At a speed of 20 mph the distance traveled in 2.4h is:

`\text{distance}=20\text{mph}\cdot2.4h=48m`Then, Miles have traveled 48 miles when they meet