Elisabeti bikes from home to the grocery store and back to pick up in- gredients. On the way to the store, she averages 15 mph. Encumbered by groceries, she averages 10 mph on the way back. What is her average speed for the whole hour?
Here average speed is 12.5 mph.
Her*
AxenMO, if you cannot explain how to do the problem, you have not helped this student. Just giving the answer is very unhelpful.
distance home to store = d
total time = 1 hr
d = 15 t
d = 10(1-t)
15 t = 10 -10 t
25 t = 10
t = 10/25
d = 15* 10/25
d = 6 miles each waay
total distance = 12 miles
total time = 1 hour
so average speed = 12 miles per hour
BY THE way AXENMO averaging the speeds them selves is NOT correct.
To find Elisabeti's average speed for the whole hour, we need to calculate the total distance she traveled and divide it by the total time taken.
Let's assume the distance from Elisabeti's home to the grocery store is 'd' miles.
On the way to the store, she averaged 15 mph. So the time taken to reach the store would be:
Time1 = Distance1 / Speed1
Time1 = d / 15
On the way back from the store, she averaged 10 mph. So the time taken to return home would be:
Time2 = Distance2 / Speed2
Time2 = d / 10
The total time taken for the whole round trip would be the sum of Time1 and Time2:
Total Time = Time1 + Time2
Now, let's substitute the values and calculate the total time:
Total Time = (d / 15) + (d / 10)
To find the average speed for the whole hour, we divide the total distance traveled by the total time taken:
Average Speed = Total Distance / Total Time
The total distance traveled is the sum of the distances from home to the store and from the store back home:
Total Distance = 2d
Now, let's substitute the values and calculate the average speed:
Average Speed = 2d / (Total Time)
Average Speed = 2d / ((d / 15) + (d / 10))
Simplifying further:
Average Speed = 2d / ((3d + 2d) / 30)
Average Speed = 60d / (5d + 6d)
Average Speed = 60d / 11d
Average Speed = 60 / 11
Therefore, Elisabeti's average speed for the whole hour is approximately 5.45 mph.