Question - Calculating Total Distance and Average Speed of a Bus Journey
Solution:
Let \( d_1 \) be the distance covered in the first 2 hours, and \( d_2 \) be the distance covered in the next 4 hours.
Given \( d_1 = 125 \) km and \( d_2 = 240 \) km.
The total distance \( D \) covered by the bus is: \( D = d_1 + d_2 \).
\( D = 125 \) km \( + 240 \) km.
\( D = 365 \) km.
Let \( t_1 \) be the time spent during the first part of the journey, and \( t_2 \) be the time spent during the second part.
Given \( t_1 = 2 \) hours and \( t_2 = 4 \) hours.
The total time \( T \) spent is: \( T = t_1 + t_2 \).
\( T = 2 \) hours \( + 4 \) hours.
\( T = 6 \) hours.
The average speed \( V \) of the bus is calculated as \( V = \frac{D}{T} \).
\( V = \frac{365 \text{ km}}{6 \text{ hours}} \).
\( V \approx 60.83 \) km/hour.
Tutor Solution:
The first step is to understand what we are being asked to calculate. However, the question itself is incomplete as it does not specify the particular calculation it's referring to, such as finding the average speed for the entire trip or for each individual segment.
Assuming we are asked to find the average speed for the entire trip, we would follow these steps:
1.Add the total distance traveled: Adam drove 125 km in the first 2 hours, and 240 km in the next 4 hours. So the total distance is:
\[ \text{Total distance} = 125\ km + 240\ km = 365\ km \] 2.Add the total time traveled: Adam drove for a total of 2 hours for the first part, and 4 hours for the second part. So the total time is:
\[ \text{Total time} = 2\ hours + 4\ hours = 6\ hours \] 3.Calculate the average speed: The average speed is the total distance divided by the total time.
\[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} \] \[ \text{Average speed} = \frac{365\ km}{6\ hours} \] 4.Perform the division to find the average speed:
\[ \text{Average speed} = \frac{365}{6}\ km/hr ≈ 60.83\ km/hr \]Hence, the average speed of Adam's trip was approximately 60.83 km/hr.
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