SOLUTION: After a certain number of men had been employed on a job for 24 days and had finished half of it, 16 more men were employed and the remaining job was completed in 16 days. How many

Algebra ->  Rate-of-work-word-problems -> SOLUTION: After a certain number of men had been employed on a job for 24 days and had finished half of it, 16 more men were employed and the remaining job was completed in 16 days. How many      Log On


   



Question 919789: After a certain number of men had been employed on a job for 24 days and had finished half of it, 16 more men were employed and the remaining job was completed in 16 days. How many men were employed first?
Found 2 solutions by ewatrrr, josmiceli:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
N%5B1%5D+%2A+T%5B1%5D+%2A+W%5B2%5D+=N%5B2%5D%2AT%5B2%5D%2AW%5B1%5D
24n = 16(n+16)
8n = 256
n = 32 men were employed at first
And...checking
32*24days = 48*16days

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = number of men employed first
+%281%2F2%29+%2F+24+=+1+%2F+48+ = the rate of working
for +n+ men
-----------------
+1%2F+%28+48n+%29+ = the rate of working for +1+ man
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Then, 16 more men were employed and the
remaining job was completed in 16 days
For +1+ man, this is a rate of:
+%281%2F2%29+%2F+%28%28+n%2B16%29%2A16+%29+
+1+%2F+%28+2%2A16%2A%28+n+%2B+16+%29+%29+
+1+%2F+%28+32n+%2B+512+%29+
--------------------------
Now I can say:
+1+%2F+%28+48n+%29+=+1+%2F+%28+32n+%2B+512+%29+
+48n+=+32n+%2B+512+
+16n+=+512+
+n+=+32+
32 men were employed first
--------------
check:
+1+%2F+%28+48n+%29+=+1+%2F+%28+32n+%2B+512+%29+
+1+%2F+%28+48%2A32+%29+=+1+%2F+%28+32%5E2+%2B+512+%29+
+1+%2F+1536+=+1+%2F+%28+1024+%2B+512+%29+
+1+%2F+1536+=+1+%2F+1536+
OK