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

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Amanda's trip involved an 8-hour drive to her destination and a 5-hour return trip that was 21% faster. The distance for both trips can be expressed in terms of speed and time, but a relationship between the speeds on both trips is necessary to solve for the total distance. Without additional information about the speed on either leg of the journey, the problem remains unsolvable. The discussion highlights the need for clarity on units of measurement to determine the distance traveled accurately. Overall, the problem illustrates the complexities of calculating distance when key variables are missing.
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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 ?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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