Mathematics

Bill can hammer 20 nails in 6 minutes. Jeff can do the same job in only 5 minutes . How long will it take them to finish if Bill hammers the first 5 nails, then Jeff hammers for 3 minutes then Bill finishes the job?
A. 4.6 minutes
B. 5.0 minutes
C. 5.4 minutes
D. 5.8 minutes
E. 6.0 minutes


Answers

BettieZumbrunnen

4 years ago Comment

Bill hammers 20 nails in 6 minutes.
==> It takes him 6/20 = 0.3 minutes to hammer one nail.
==> If the total job is 20 nails, then he does 1/6 of the job in 1 minute.

Jeff hammers 20 nails in 5 minutes.
==> It takes him 5/20 = 0.25 minutes to hammer one nail.
==> If the total job is 20 nails, then he does 1/5 of the job in 1 minute.

Notice that the question doesn't say what size job they're assigned.
I'll assume it's a 20-nail job.

First step: Bill hammers 5 nails.
At 0.3 minutes per nail, that takes Bill 5 x 0.3 = 1.5 minutes

Second step:  Jeff hammers for 3 minutes.
At 0.25 minute per nail, he adds 3/0.25 = 12 nails to Bill's 5, for a total of 17 so far.

Third step:  Bill finishes the job.
There are (20 - 17) = 3 nails left to go.
At 0.3 minutes per nail, this takes Bill 3 x 0.3 = 0.9 minutes.

First step . . . . .  1.5 minutes
Second step . . . 3    minutes
Third step . . . . . 0.9 minutes
Total . . . . . . . . . 5.4 minutes