Every day, to avoid traffic during her morning commute, Yunru takes the backroads from her home to her workplace. There is less traffic during the afternoon commute home from her workplace, so she always takes the highway instead of the backroads. Taking the backroads is 7 miles longer than taking the highway, and her total commute distance is 57 miles long. How many miles long is her morning commute?

Every day, to avoid traffic during her morning commute, Yunru takes the backroads from her home to her workplace. There is less traffic during the afternoon commute home from her workplace, so she always takes the highway instead of the backroads. Taking the backroads is 7 miles longer than taking the highway, and her total commute distance is 57 miles long. How many miles long is her morning commute?

Answer

First, let's identify the two parts of Yunru's commute. The morning commute is via backroads and the afternoon commute is via the highway. Let 'x' represent the distance of the highway (the afternoon commute). Since the backroads (the morning commute) are 7 miles longer than the highway, the morning commute distance can be represented as 'x + 7'. The problem states that the total commute distance for the day (morning plus afternoon) is 57 miles. We can set up the following equation: (morning commute) + (afternoon commute) = total distance. This translates to (x + 7) + x = 57. Combining like terms, we get 2x + 7 = 57. Subtracting 7 from both sides gives 2x = 50. Dividing by 2, we find x = 25. This means the highway is 25 miles long. Since the question asks for the length of her morning commute (the backroads), we calculate x + 7, which is 25 + 7 = 32 miles. Therefore, Yunru's morning commute is 32 miles long.