Jennifer travels from Boston , Massachusetts, to Fairfield, Connecticut, a distance of 90 miles, at a speed of 45 miles per hour, and returns at a speed of 60 miles per hour. To the nearest half mile per hour, what is Jennifer's average rate for the whole trip?
A) 50 1/2
B) 51
C) 51 1/2
D) 52 1/2
E) 53 1/2
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To find Jennifer's average rate for the whole trip, we need to calculate the total time she spent traveling and the total distance she covered during the whole trip. Then, we can divide the total distance by the total time to find the average rate.
First, let's find the time it took Jennifer to travel from Boston to Fairfield. We can use the formula: time = distance / speed.
Time (to Fairfield) = 90 miles / 45 miles per hour = 2 hours.
Next, let's find the time it took Jennifer to return from Fairfield to Boston. We can again use the formula: time = distance / speed.
Time (return) = 90 miles / 60 miles per hour = 3/2 hours.
Now, let's calculate the total time for the whole trip. The total time is the sum of the time it took Jennifer to travel to Fairfield and the time it took her to return.
Total time = Time (to Fairfield) + Time (return)
= 2 hours + 3/2 hours
= 4 1/2 hours.
Next, let's calculate the total distance covered during the whole trip. The total distance is twice the distance between Boston and Fairfield.
Total distance = 2 * 90 miles = 180 miles.
Finally, let's find the average rate for the whole trip by dividing the total distance by the total time.
Average rate = Total distance / Total time
= 180 miles / 4 1/2 hours
= 180 miles / 9/2 hours
= 180 miles * 2/9 hours
= 40 miles per hour.
To the nearest half mile per hour, Jennifer's average rate for the whole trip is 40 miles per hour.
Therefore, the correct option is not present among the given answer choices.
average rate = total distance / total time
to find the time for one leg of the trip ... time = distance / rate