Question - Calculating Average Speed of Mary's Motorcycle Ride
Solution:
To find the average speed, we need to calculate the total distance traveled and the total time taken.
Total distance = 35 km + 105 km = 140 km
Total time = 0.5 hours (30 minutes) + 1.5 hours = 2 hours
Average speed = \(\frac{\text{Total distance}}{\text{Total time}}\)
Average speed = \(\frac{140 \text{ km}}{2 \text{ hours}} = 70 \text{ km/hour}\)
Tutor Solution:
\[ \text{Average Speed} = \frac{\text{Distance}}{\text{Time}} \]
For the first part of her journey:\[ \text{Average Speed for the first 30 minutes} = \frac{35 \text{ km}}{0.5 \text{ hours}} \]
Here, I have converted 30 minutes into hours because speed is conventionally measured in km per hour.\[ \text{Average Speed for the first 30 minutes} = \frac{35}{0.5} = 70 \text{ km/h} \]
For the second part of her journey:\[ \text{Average Speed for the next 1.5 hours} = \frac{105 \text{ km}}{1.5 \text{ hours}} \]
\[ \text{Average Speed for the next 1.5 hours} = \frac{105}{1.5} = 70 \text{ km/h} \]
If the question sought to find the average speed for the entire journey, we would combine both parts. We'll calculate the total distance and the total time, then divide the former by the latter:Total distance = 35 km + 105 km = 140 km
Total time = 0.5 hours + 1.5 hours = 2 hours
\[ \text{Overall Average Speed} = \frac{140 \text{ km}}{2 \text{ hours}} = 70 \text{ km/h} \]
So, Mary's average speed for each part of her journey, and for the entire trip, is 70 km/h.CamTutor
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