1971 AMC 12 Problem 34

Attempt Problem 34 of the 1971 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 1971 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

34.

An ordinary clock in a factory is running slow so that the minute hand passes the hour hand at the usual dial positions (1212 o’clock, etc.) but only every 6969 minutes. At time and one-half for overtime, the extra pay to which a $4.00\$4.00-per-hour worker should be entitled after working a normal 88-hour day by that slow-running clock is:

$2.30\$2.30

$2.60\$2.60

$2.80\$2.80

$3.00\$3.00

$3.30\$3.30

Answer: B
Concepts:clockratemoneyratio and proportion
Difficulty rating: 1850
Small Hint:

A normal clock’s hands pass every 72011\frac{720}{11} minutes

Big Hint:

Eleven slow-clock intervals total 1212 displayed hours but 1212 hours 3939 minutes of real time

Solution:

Successive hand-overlaps are 72011\frac{720}{11} real minutes apart, while this slow clock displays 6969 minutes between them. Thus 1212 displayed hours correspond to 759759 real minutes, since 1169=759=1260+39. 11\cdot69=759=12\cdot60+39. Eight displayed hours therefore take 88 hours 2626 minutes, so the overtime is 2626 minutes. At $6\$6 per hour, that pays $2.60.\$2.60.

Therefore, the correct answer is B.

← Problem 33#33
Full Exam

Problem 34 in Other Years

1950 AMC 12 · 1951 AMC 12 · 1952 AMC 12 · 1953 AMC 12 · 1954 AMC 12 · 1955 AMC 12 · 1956 AMC 12 · 1957 AMC 12 · 1958 AMC 12 · 1959 AMC 12 · 1960 AMC 12 · 1961 AMC 12 · 1962 AMC 12 · 1963 AMC 12 · 1964 AMC 12 · 1965 AMC 12 · 1966 AMC 12 · 1967 AMC 12 · 1968 AMC 12 · 1969 AMC 12 · 1970 AMC 12 · 1972 AMC 12 · 1973 AMC 12