Three students use calligraphy pens to write the names of graduating seniors on their diplomas. One writes 7 names in 6 minutes, another writes 17 names in 10 minutes, and the third writes 23 names in 15 minutes. How long, to the nearest minute, will the students take to write names on 440 diplomas if they work together?
PS: This is a multiple choice problem, but the answer I got is not in the four choices. The four choices are 97 minutes, 100 minutes, 103 minutes, and 290 minutes.
The LCM of 6 minutes, 10 minutes, and 15 minutes is 30 minutes.
Suppose all of them worked together for 30 minutes.
Then:
The student who writes 7 names in 6 minutes will write 35 names in 30 minutes.
The student who writes 17 names in 10 minutes will write 51 names in 30 minutes.
The student who writes 23 names in 15 minutes will write 46 names in 30 minutes.
Therefore in 30 minutes, they will write 35+51+46 or 132 names.
So we set up a proportion:
132 names is to 440 names as 30 minutes is to x minutes:
=
132x = 13200
x = 100 minutes.
Edwin