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 15 mph. With less traffic on his return home, he drove 25 mph. If the entire travel time took him four hours, how long did it take him to get to the comic book store? Enter your answer in hours and rounded to one decimal place if needed.

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SemaF434771 SemaF434771 · Answer 1 · 2022-10-27T15:23:46+02:00

Since the rule of distance is

[tex]d=v\times t[/tex]

Where v is the speed and t is the time

Since the distance from home to the book store is equal to the distance from the book store to the home, then

Let the distance = d

Since the speed in the going way is 15 mph, then

[tex]t_1=\frac{d}{15}[/tex]

Since the speed in the back way is 25 mph, then

[tex]t_2=\frac{d}{25}[/tex]

Since the time of the entire trip is 4 hours, then

[tex]t_1+t_2=4[/tex]

Substitute the values of t1 and t2

[tex]\frac{d}{15}+\frac{d}{25}=4[/tex]

Multiply both sides by 75 (L.C.M of 15 and 25)

[tex]\begin{gathered} \frac{d}{15}(75)+\frac{d}{25}(75)=4(75) \\ 5d+3d=300 \\ 8d=300 \end{gathered}[/tex]

Divide both sides by 8

[tex]\begin{gathered} \frac{8d}{8}=\frac{300}{8} \\ d=37.5m \end{gathered}[/tex]

Substitute d by 37.5 in t1 to find it

[tex]\begin{gathered} t_1=\frac{37.5}{15} \\ t_1=2.5h \end{gathered}[/tex]

It took him 2.5 hours to get to the book store