You and a friend work at an orange orchard. It takes you 40 minutes to pick all of the oranges from the tree. It takes your friend 60 minutes to complete the same job. How long will it take to pick all of the oranges from an orange tree if you work together?
I think it is 50 minutes, because in the middle of 40 and 60 is 50. But I'm not sure if that is correct. And I also don't know how to solve the problem.
Thank You! ~KyraXxx
ratecombined=rate1+rate2
ratecombined=all/40min+all/60 min
= (60all+40all)/2400=100*all/2400
= all/24
so together, all can be picked in 24 minutes.
To solve this problem, you can use the concept of rates.
First, let's find the rate at which each person picks oranges. We know that you can pick all the oranges in 40 minutes, so your rate is 1 tree / 40 minutes. Similarly, your friend's rate is 1 tree / 60 minutes.
When you work together, you are combining your rates. To do this, add your rates together, resulting in a combined rate of:
1 tree / 40 minutes + 1 tree / 60 minutes = (3/120 + 2/120) trees / minute = 5/120 trees / minute
Now, we can find how long it would take to pick all the oranges working together by dividing the total number of trees (which is 1 in this case) by the combined rate:
1 tree / (5/120 trees / minute) = (1 * 120 / 5) minutes = 24 minutes
Therefore, it would take you and your friend 24 minutes to pick all of the oranges from the tree if you work together.