A bee gathered nectar for 3/4 of an hour it returned to the hive every 1/12th hour. How many trips did the bee make.
1/12 hour = 5 minutes
3/4 hour = 45 minutes
45/5 = ?
To calculate the number of trips the bee made, we need to find the total time it spent going back and forth between gathering nectar and returning to the hive.
Let's calculate the time spent for each part separately:
Time spent gathering nectar = 3/4 of an hour
Time spent returning to the hive = 1/12 of an hour
We can now calculate how many times the bee made a complete trip by dividing the time spent gathering nectar by the total time taken for each trip.
Total time taken for each trip = Time spent gathering nectar + Time spent returning to the hive
Given that the time spent gathering nectar is 3/4 of an hour and the time spent returning to the hive is 1/12 of an hour, we have:
Total time taken for each trip = 3/4 + 1/12
To add these fractions, we need to find a common denominator. In this case, the least common multiple of 4 and 12 is 12.
Therefore:
Total time taken for each trip = (3/4) + (1/12)
= (9/12) + (1/12)
= 10/12
= 5/6
Now, we can calculate the number of trips by dividing the time spent gathering nectar by the total time taken for each trip:
Number of trips = Time spent gathering nectar ÷ Total time taken for each trip
Given that the time spent gathering nectar is 3/4 of an hour and the total time taken for each trip is 5/6 of an hour, we have:
Number of trips = (3/4) ÷ (5/6)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
Number of trips = (3/4) * (6/5)
= (3 * 6) / (4 * 5)
= 18 / 20
= 9 / 10
Therefore, the bee made 9/10 of a trip or 0.9 trips.