While walking from her house to school, Miriam walks at a pace of 5 km/h. When she walks in the hallways at school, she slows down to 3 ½ km/h.
If she spent 2 ½ hours walking to and from school and ¾ of an hour walking in the hallways, what was her average walking speed?
[(10/4 * 5) + (3/4 * 7/2)] / (10/4 + 3/4)
To find Miriam's average walking speed, we need to calculate the total distance she walked and divide it by the total time it took.
First, let's calculate the distance Miriam walks from her house to school. She walks at a pace of 5 km/h for 2 ½ hours. The formula to calculate distance is:
Distance = Speed * Time
Distance = 5 km/h * 2.5 hours
Distance = 12.5 km
Next, let's calculate the distance Miriam walks in the hallways. She walks at a slower pace of 3 ½ km/h for ¾ of an hour. Again, using the distance formula:
Distance = Speed * Time
Distance = 3.5 km/h * 0.75 hours
Distance = 2.625 km
Now, let's calculate the total distance Miriam walked. She walks the distance from her house to school twice because she walks there and back:
Total Distance = 2 * (Distance from house to school)
Total Distance = 2 * 12.5 km
Total Distance = 25 km
Next, let's calculate the total time Miriam spent walking:
Total Time = Time to and from school + Time in hallways
Total Time = 2.5 hours + 0.75 hours
Total Time = 3.25 hours
Finally, let's calculate the average walking speed by dividing the total distance by the total time:
Average Speed = Total Distance / Total Time
Average Speed = 25 km / 3.25 hours
Average Speed ≈ 7.69 km/h
Therefore, Miriam's average walking speed is approximately 7.69 km/h.