Question

adwick drives into the city to buy the most recent issue of Black Panther at a comicok store. On the way there he drove 45 miles per hour. With more traffic on his returnome, he drove 35 miles per hour. If the entire travel time took him 4 hours, how longd it take him to get to the comic book store? Enter your answer in hours and roundedone decimal place if needed.hours

Answer 1

From the statement we know that:

• the total distance travelled is 2d, being d the distance to the comic store,

,

• the forward velocity is v1 = 45 ml/h,

,

• the backward velocity is v2 = 35 ml/h,

,

• the total time spent on the travel is t = 4 h.

Now, we can write the total distance travelled in the following way:

$\begin{gathered} 2d=v_1\cdot t_1+v_2\cdot t_2 \\ 2d=v_1\cdot t_1+v_2\cdot(t-t_1) \\ 2d=(v_1-v_2)\cdot t_1+v_2\cdot t \end{gathered}$

Where:

• t1 is the time for the travel to the comic book store,

,

• t2 is the time for the return from the comic book store.

Now, we also know that the distance is equal to the product between the time and the velocity, so:

$d=v_1\cdot t_1\text{.}$

Replacing the last equation in the equation above, we have:

$2\cdot v_1\cdot t_1=(v_1-v_2)\cdot t_1+v_2\cdot t\text{.}$

Now, we solve the last equation for v1:

$\begin{gathered} 2\cdot v_1\cdot t_1=(v_1-v_2)\cdot t_1+v_2\cdot t_{} \\ 2\cdot v_1\cdot t_1-(v_1-v_2)\cdot t_1=v_2\cdot t_{} \\ (v_1+v_2)\cdot t_1=v_2\cdot t \\ t_1=\frac{v_2}{v_1+v_2}\cdot t\text{.} \end{gathered}$

Replacing the values of the velocities v1 and v2, and the time t we get:

$\begin{gathered} t_1=\frac{45ml/h}{45ml/h+35ml/h}\cdot4h \\ t_1=2.25h \\ t_1\cong2.3h \end{gathered}$

Answer

Rounded to one decimal place, it takes 2.3 hours to get to the comic book store.