1956 AMC 12 Problem 47

Attempt Problem 47 of the 1956 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1956 AMC 12 solutions, or check the answer key.

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47.

An engineer said he could finish a highway section in 33 days with his present supply of a certain type of machine. However, with 33 more of these machines the job could be done in 22 days. If the machines all work at the same rate, how many days would it take to do the job with one machine?

66

1212

1515

1818

3636

Answer: D
Concepts:work ratesinverse proportionlinear equation
Difficulty rating: 1490
Small Hint:

Let mm be the present number of machines and measure work in machine-days

Big Hint:

Equate 3m3m with 2(m+3)2(m+3)

Solution:

If there are presently mm machines, the job requires 3m3m machine-days. With three more machines it requires 2(m+3)2(m+3) machine-days, so 3m=2(m+3), 3m=2(m+3), giving m=6.m=6. The job therefore requires 3m=183m=18 machine-days, so one machine would take 1818 days.

Thus, the correct answer is D.

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Problem 47 in Other Years

1950 AMC 12 · 1951 AMC 12 · 1952 AMC 12 · 1953 AMC 12 · 1954 AMC 12 · 1955 AMC 12 · 1957 AMC 12 · 1958 AMC 12 · 1959 AMC 12