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To solve this problem, we can use the formula: distance = speed × time.
Let's denote:
- \( t_w \): time taken to walk to school.
- \( t_b \): time taken to ride the bicycle to school.
We know that the distance to school is the same whether Thoriso walks or rides her bicycle.
So, if Thoriso walks to school at 5 km/h, the time it takes her to get to school is:
\[ t_w = \frac{{\text{distance}}}{{\text{speed}}} = \frac{{\text{distance}}}{{5 \, \text{km/h}}} \]
If Thoriso rides her bicycle at 15 km/h, the time it takes her to get to school is:
\[ t_b = \frac{{\text{distance}}}{{15 \, \text{km/h}}} \]
Given that it takes her 10 minutes to get home on her bicycle, we can express this as:
\[ t_b - \frac{{10 \, \text{minutes}}}{{60 \, \text{minutes/hour}}} = \frac{{\text{distance}}}{{15 \, \text{km/h}}} - \frac{1}{6} \]
We know that the distance to school is the same in both cases, so \( t_w = t_b - \frac{1}{6} \).
Now, we can equate \( t_w \) and \( t_b \):
\[ \frac{{\text{distance}}}{{5 \, \text{km/h}}} = \frac{{\text{distance}}}{{15 \, \text{km/h}}} - \frac{1}{6} \]
We can solve this equation to find the distance.
\[ \frac{1}{5} = \frac{1}{15} - \frac{1}{6} \]
\[ \frac{1}{5} = \frac{1}{15} - \frac{5}{30} \]
\[ \frac{1}{5} = \frac{1}{30} \]
\[ \text{The distance is } 6 \text{ km} \]
Now that we know the distance, we can calculate the time it takes Thoriso to walk to school:
\[ t_w = \frac{6 \, \text{km}}{5 \, \text{km/h}} = 1.2 \, \text{hours} = 1 \, \text{hour} \, 12 \, \text{minutes} \]
So, Thoriso takes 1 hour and 12 minutes to walk to school.
Let's denote:
- \( t_w \): time taken to walk to school.
- \( t_b \): time taken to ride the bicycle to school.
We know that the distance to school is the same whether Thoriso walks or rides her bicycle.
So, if Thoriso walks to school at 5 km/h, the time it takes her to get to school is:
\[ t_w = \frac{{\text{distance}}}{{\text{speed}}} = \frac{{\text{distance}}}{{5 \, \text{km/h}}} \]
If Thoriso rides her bicycle at 15 km/h, the time it takes her to get to school is:
\[ t_b = \frac{{\text{distance}}}{{15 \, \text{km/h}}} \]
Given that it takes her 10 minutes to get home on her bicycle, we can express this as:
\[ t_b - \frac{{10 \, \text{minutes}}}{{60 \, \text{minutes/hour}}} = \frac{{\text{distance}}}{{15 \, \text{km/h}}} - \frac{1}{6} \]
We know that the distance to school is the same in both cases, so \( t_w = t_b - \frac{1}{6} \).
Now, we can equate \( t_w \) and \( t_b \):
\[ \frac{{\text{distance}}}{{5 \, \text{km/h}}} = \frac{{\text{distance}}}{{15 \, \text{km/h}}} - \frac{1}{6} \]
We can solve this equation to find the distance.
\[ \frac{1}{5} = \frac{1}{15} - \frac{1}{6} \]
\[ \frac{1}{5} = \frac{1}{15} - \frac{5}{30} \]
\[ \frac{1}{5} = \frac{1}{30} \]
\[ \text{The distance is } 6 \text{ km} \]
Now that we know the distance, we can calculate the time it takes Thoriso to walk to school:
\[ t_w = \frac{6 \, \text{km}}{5 \, \text{km/h}} = 1.2 \, \text{hours} = 1 \, \text{hour} \, 12 \, \text{minutes} \]
So, Thoriso takes 1 hour and 12 minutes to walk to school.
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