Calculating Distance Traveled: Solving for the Unknown in a Multi-Unit Problem

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The discussion centers on a multi-unit problem involving distance calculation for Amanda's trips. Amanda's outbound trip took 8 hours at a speed of v_1, while her return trip took 5 hours at a speed 21% faster, denoted as v_2. The equations derived are D = v_1 * 8 for the outbound trip and D = v_2 * 6.32 for the return trip, indicating a need for a relationship between v_1 and v_2 to solve for the distance D. The participants highlight that without additional information, such as the specific speed or distance units, the problem remains unsolvable.

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My problem. Amanda took an 8 hour drive. The return trip home took 5 hours and was 21% faster. How many miles did she drive?
 
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There isn't enough information. Is this the whole problem?

Trip out:
[math]D = v_1 t_1 = 8 v_1[/math]

Trip back:
[math]D = v_2 t_2 = v_2 \left [ (1 - .21) t_1 \right ] = 6.32 v_2[/math]

We need some other relationship between [math]v_1[/math] and [math]v_2[/math].

-Dan
 
You can see immediately that something is missing. Imagine you can find a solution $D$ for the distance. How would you known if this represents miles, kilometers, or some other unit ?
 

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