Nico drives from school to the store at 25 miles per hour. He drives back to the school (along the same route) at 35 miles per hour, and the returns to the store (via the same route) travelling at 40 miles per hour. Find the average rate for the three trips. Round your answer to the nearest mile per hour.
I know the answer isn't 25+35+40/3=33mph.
Why isn't that the answer?
To find the average rate for the three trips, we need to calculate the total distance traveled and then divide it by the total time taken.
Let's assume the distance from the school to the store is "d" miles.
For the first trip, Nico drives from school to the store at 25 miles per hour. The time taken for this trip can be calculated using the formula:
Time = Distance / Speed
So the time taken for the first trip is d / 25.
For the second trip, Nico drives back to the school at 35 miles per hour. The time taken for this trip is:
Time = Distance / Speed
Since it's the same distance as the first trip, the time taken for the second trip is also d / 35.
Finally, for the third trip, Nico returns to the store traveling at 40 miles per hour. The time taken for this trip is:
Time = Distance / Speed
Again, since it's the same distance, the time taken for the third trip is d / 40.
Now, to calculate the average rate, we need to find the total distance and total time.
Total distance = Distance of the first trip + Distance of the second trip + Distance of the third trip
= d + d + d
= 3d
Total time = Time taken for the first trip + Time taken for the second trip + Time taken for the third trip
= d / 25 + d / 35 + d / 40
Now, we can calculate the average rate:
Average Rate = Total Distance / Total Time
= 3d / (d/25 + d/35 + d/40)
Simplifying the expression:
Average Rate = 3d / ((35d + 25d + 40d)/(35*25*40))
= 3d / (100d/35)
= 105 / 4
Rounding to the nearest mile per hour, the average rate for the three trips is approximately 26 mph.