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Sagot :
The given information is:
Andrea is 108 miles away from Destiny.
Destiny travels 9 mph faster than Andrea.
They meet after 4 hours.
Let's convert that information into equations:
Let's call x the distance that Destiny travels to find Andrea and y the distance Andrea travels to find Destiny, then:
[tex]x+y=180\text{ Eq. (1)}[/tex]If they meet after 4 hours, the equation for the distance Destiny traveled is:
[tex]\text{velocity}\cdot\text{time}=\text{distance}[/tex]But the problem also says that Destiny travels 9 mph faster than Andrea, then let's call z the mph that Andrea is traveling, thus:
[tex](z+9)\cdot4=x\text{ Eq. (2)}[/tex]And the equation for the distance Andrea traveled is:
[tex]z\cdot4=y\text{ Eq.(3)}[/tex]Then you have a system of 3 equations and 3 variables.
Let's solve it to find how fast each was traveling.
From equation 3 you know that y=4z. You can replace the y-value into equation 1, you will obtain:
[tex]x+4z=180\text{ Eq. (4)}[/tex]Next, you can solve for x in terms of z, from equation 4:
[tex]x=180-4z\text{ Eq.(5)}[/tex]Replace the x-value into equation 2 and solve for z:
[tex]\begin{gathered} (z+9)\cdot4=180-4z \\ \text{Apply distributive property} \\ 4z+36=180-4z \\ \text{Add 4z to both sides} \\ 4z+36+4z=180-4z+4z \\ 8z+36=180 \\ \text{Subtract 36 from both sides} \\ 8z+36-36=180-36 \\ 8z=144 \\ \text{Divide both sides by 8} \\ \frac{8z}{8}=\frac{144}{8} \\ z=18 \end{gathered}[/tex]Then if z=18 mph, this is how fast Andrea is traveling.
And Destiny travels 9 mph faster than Andrea, then Destiny travels at (z+9)=18+9=27 mph
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