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Chadwick drives into the city to buy the most recent issue of Black Panther at a comic book store. On the way there he drove 25 miles per hour. With more traffic on his return home, he drove 15 miles per hour. If the entire travel time took him 4 hours, how long did it take him to get to the comic book store? Enter your answer in hours and round to one decimal place if needed.

Respuesta :

[tex]\text{distance}=\text{speed}\cdot\text{time}[/tex]

Let x be the time it takes him to get to the comic book store

Ley y be the time it takes him to return home

The distance is the sa from home to comic book store and from comic book store to home:

[tex]25mi/h\cdot x=15mi/h\cdot y[/tex]

The entire travel time was 4 hours:

[tex]x+y=4[/tex]

Uset he next system of equations:

[tex]\begin{gathered} 25x=15y \\ x+y=4 \end{gathered}[/tex]

1. Solve y in the first equation:

[tex]\begin{gathered} \frac{25x}{15}=\frac{15}{15}y \\ \\ \frac{5}{3}x=y \\ \\ \\ y=\frac{5}{3}x \end{gathered}[/tex]

2. Use the value of y you get in step 1 in the second equation.

[tex]x+\frac{5}{3}x=4[/tex]

3. Solve x:

[tex]\begin{gathered} \frac{3x+5x}{3}=4 \\ \\ \frac{8x}{3}=4 \\ \\ 3\cdot\frac{8}{3}x=3\cdot4 \\ \\ 8x=12 \\ \\ \frac{8}{8}x=\frac{12}{8} \\ \\ x=1.5 \end{gathered}[/tex]

Then, the time it takes him to get to the comic book store is 1.5 hours

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