1956 AMC 12 Problem 22

Attempt Problem 22 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.

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

22.

Jones covered a distance of

50

miles on his first trip. On a later trip he traveled

300

miles while going three times as fast. His new time compared with the old time was:

three times as much

twice as much

the same

half as much

a third as much

Write each travel time as distance divided by speed

If the old speed is

v,

compare

\frac{50}{v}

with

\frac{300}{3v}

If the first speed was

v,

the old time was

\frac{50}{v}.

The later time was

\frac{300}{3v}=\frac{100}{v}=2\left(\frac{50}{v}\right).

Thus the new time was twice the old time.

The correct answer is B.

Problem 22 in other years