Respuesta :
Given that:
- Megan cycles from home to school at a speed of 16 kilometers per hour.
- Megan cycles back on the same route at a speed of 15 kilometers per hour.
- The total time is:
[tex]7\frac{3}{4}h[/tex]You know that "d" represents the distance (in kilometers) from Megan's house to school.
1. In order to solve this exercise, you need to remember the following formula:
[tex]d=V\cdot t[/tex]Where "d" is distance, "V" is speed, and "t" is time.
2. In this case, you know that from home to school the speed (in kilometers per hour) is:
[tex]V_1=16[/tex]And from school to home:
[tex]V_2=15[/tex]3. By definition:
[tex]t=\frac{d}{V}[/tex]Where "d" is distance, "V" is speed, and "t" is time.
4. Then, from home to school you can set up that time taken is:
[tex]t_1=\frac{d}{16}[/tex]5. Since she took the same route, the distance from school to home is the same as the distance from home to school. Then:
[tex]t_2=\frac{d}{15}[/tex]6. Then total time can be represented as:
[tex]t_t=\frac{d}{16}+\frac{d}{15}[/tex]Knowing the value of the total time, you get this equation that can be used to find the distance "d" :
[tex]\frac{d}{16}+\frac{d}{15}=7\frac{3}{4}[/tex]7. Since:
[tex]\frac{3}{4}=0.75[/tex]You can rewrite the equation in this form:
[tex]\frac{d}{16}+\frac{d}{15}=7.75[/tex]8. Now you can solve for "d":
[tex]\begin{gathered} \frac{15d+16d}{(16)(15)}=7.75 \\ \\ \frac{31d}{240}=7.75 \end{gathered}[/tex][tex]\begin{gathered} d=7.75\cdot\frac{240}{31} \\ \\ d=\frac{1860}{31} \end{gathered}[/tex][tex]d=60[/tex]9. Having the distance from school to home and from home to school, you can set up this equation for the total distance (in kilometers):
[tex]D=2d[/tex]10. Substituting the value of "d" into the equation, you get:
[tex]D=2(60)=120[/tex]Hence, the answer is:
- Equation:
[tex]D=2d[/tex]- Total distance:
[tex]D=120\operatorname{km}[/tex]
