Elena Plescan wrote:Hi,
There is a problem I have doubts about.

Danny and Ian are munching on a jar full of candies. Had Danny eaten alone it would have taken him 5 minutes to finish the candies in the jar. Had Ian eaten alone it would have taken him 10 minutes to finish half the jar.

Since both of them are eating simultaneously, how long would it take them to empty the jar?

2.5 minutes
3 minutes
3 minutes and 20 seconds
6 minutes and 40 seconds
4 minutes

Let the number of candies in the jar = 20.
Since Danny can empty the jar in 5 minutes, Danny's rate = w/t = 20/5 = 4 candies per minute.
Since Ian can empty half the jar -- 10 candies -- in 10 minutes, Ian's rate = w/t = 10/10 = 1 candy per minute.
Combined rate for Danny and Ian = 4+1 = 5 candies per minute.
Thus:
At a combined rate of 5 candies per minute, the time for Danny and Ian to empty the whole jar of 20 candies = w/r = 20/5 = 4 minutes.

The correct answer is E..

However, if the apply the work formula, it results that
1/D+1/I=1/Total time
1/5+1/10=1/Tt
15/50=1/Tt
Tt=50/15=3 1/3 OR 3 mins 20 sec

The fraction in red is incorrect.
Since it would take Ian 10 minutes to eat HALF the jar, his time to eat the ENTIRE jar = 20 minutes.
Thus, Ian's rate = 1/20.

Adding together Danny's rate (1/5) and Ian's rate (1/20) to yield their combined rate (1/T), we get:
1/5 + 1/20 = 1/T
4/20 + 1/20 = 1/T
5/20 = 1/T
1/4 = 1/T
T = 4.

Mitch,

Thanks for the explanation. I really need to be more careful when reading texts.

Elena