Question

Andrea is 108 miles away from Destiny. They are traveling towards each other. If Destiny travels 9 mph faster than Andrea and they meet after 4 hours, how fast was each traveling?

Answer 1

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:

`x+y=180\text{ Eq. (1)}`

If they meet after 4 hours, the equation for the distance Destiny traveled is:

`\text{velocity}\cdot\text{time}=\text{distance}`

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:

`(z+9)\cdot4=x\text{ Eq. (2)}`

And the equation for the distance Andrea traveled is:

`z\cdot4=y\text{ Eq.(3)}`

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:

`x+4z=180\text{ Eq. (4)}`

Next, you can solve for x in terms of z, from equation 4:

`x=180-4z\text{ Eq.(5)}`

Replace the x-value into equation 2 and solve for z:

`\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} \\ (8z)/(8)=(144)/(8) \\ z=18 \end{gathered}`

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