Question

Megan cycles from home to school at a speed of 16 kilometers per hour. She cycles back on the same route at a speed of 15 kilometers per hour. The total time taken for the journey is 7 3/4 hours. Given that the distance from her house to school is d kilometers, write and solve an equation to find the total distance that Megan travels.

Answer 1

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:

`7(3)/(4)h`

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:

`d=V\cdot t`

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:

`V_1=16`

And from school to home:

`V_2=15`

3. By definition:

`t=(d)/(V)`

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:

`t_1=(d)/(16)`

5. Since she took the same route, the distance from school to home is the same as the distance from home to school. Then:

`t_2=(d)/(15)`

6. Then total time can be represented as:

`t_t=(d)/(16)+(d)/(15)`

Knowing the value of the total time, you get this equation that can be used to find the distance "d" :

`(d)/(16)+(d)/(15)=7(3)/(4)`

7. Since:

`(3)/(4)=0.75`

You can rewrite the equation in this form:

`(d)/(16)+(d)/(15)=7.75`

8. Now you can solve for "d":

`\begin{gathered} (15d+16d)/((16)(15))=7.75 \\ \\ (31d)/(240)=7.75 \end{gathered}`
`\begin{gathered} d=7.75\cdot(240)/(31) \\ \\ d=(1860)/(31) \end{gathered}`
`d=60`

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):

`D=2d`

10. Substituting the value of "d" into the equation, you get:

`D=2(60)=120`

Hence, the answer is:

- Equation:

`D=2d`

- Total distance: