Algebra Word problem

[soursnows]

Samantha and Ariel live 5 miles apart. They leave their houses at the same time and walk toward each other until they meet. Samantha walks at 4 mph, and Ariel walks at 3 mph.
a. How long, in minutes, will it take them to meet?
b. How far will each of them walk in that time?
-So far I’ve figured out that it will take Sam 20 minutes and Ariel 15 minutes for them to meet.. I’m not quite sure if that’s even right, could someone help?

 

[Loren]

Samantha and Ariel live 5 miles apart. They leave their houses at the same time and walk toward each other until they meet. Samantha walks at 4 mph, and Ariel walks at 3 mph.
a. How long, in minutes, will it take them to meet?
b. How far will each of them walk in that time?
-So far I’ve figured out that it will take Sam 20 minutes and Ariel 15 minutes for them to meet.. I’m not quite sure if that’s even right, could someone help?

I would draw a line segment with A at one end to indicate the point where Ariel started and S at the other end to indicate where Samantha started. The length of the segment represents 5 miles. Since Samantha walks faster than Ariel, she will cover more ground than Ariel. I would place a point on the line to represent where they will meet. Will this point be exactly in the middle of the segment? Will it be closer to A or to S? Label the point M to represent "Meeting" point. We now have segment AS with a point M which divides AS into two segments, AM and MS. Label one segment, say AM, d to represent the distance traveled by Ariel. Because the whole segment AS is 5 miles, can you now label MS in terms of d? You should label MS "5-d". Do you know why? Now, use the fact that distance = rate X time to build two equations. One of the equations will be d = 3t where t represents the time it takes for them to meet. Can you build the other equation? After you do so, you will have two equations in two unknowns. Solve for t. This will be in terms of hours. Now, convert that to minutes and go from there.

 

[mmm4444bot]

I’ve figured out that it will take Sam 20 minutes and Ariel 15 minutes for them to meet.

Their walking times cannot be different because they both left their respective house at the same time.

In other words, each of them walked exactly the same number of minutes.

You did not show any work, so I'm not sure what you're thinking.

Each of the distances traveled (one by Samantha and one by Ariel) can be expressed as the product of the elapsed time in hours multiplied by their respective rate in mph, yes?

I mean, that's the famous formula:

Distance = Time * Rate

The two expressions (Time * Rate) which represent their respective distances must add up to 5 miles.

Their walking time is unknown, so we need to choose a symbol to represent it. Otherwise, how can we write anything ?

Let t = the walking time (in hours)

So, using the famous formula, Samantha's distance is expressed as 4t and Ariel's distance is expressed as 3t. These two distances sum to 5.

Solve that equation for t, and then convert to minutes.

For part (b), you can use your result for t in hours. 4t is one distance, and 3t is the other.

 

[soroban]

Hello, soursnows!

Samantha and Ariel live 5 miles apart.
They leave their houses at the same time and walk toward each other until they meet.
Samantha walks at 4 mph, and Ariel walks at 3 mph.

(a) How long, in minutes, will it take them to meet?
(b) How far will each of them walk in that time?

They are walking toward each other at a combined speed of 7 mph.

How long will it take for them to cover 5 miles?

. . \(\displaystyle \frac{5}{7}\text{ hours} \quad\Rightarrow\quad \frac{300}{7} \:=\:42\tfrac{6}{7}\text{ minutes}\) .(a)


\(\displaystyle \begin{array}{cccccc}\text{Samantha walked at 4 mph for }\tfrac{5}{7}\text{ hours:} & 4 \times \frac{5}{7} &=& \frac{20}{7} &=& 2\frac{6}{7}\text{ miles} \\ \\[-3mm] \text{Ariel walked at 3 mph for }\frac{5}{7}\text{ hours:} & 3 \times \frac{5}{7} &=& \frac{15}{7} &=& 2\frac{1}{7}\text{ miles.} \end{array}\) .(b)