Track / Stage 4 / 331 of 340 #591 of 1964

Problem 591

AMC 12 late, AIME early

Algebra Difficulty 5.0 Find the answer

$2 \cdot 74$ a stone is dropped into a well, and the sound of the stone hitting the bottom is heard 7.7 seconds later. If the distance the stone falls in $t$ seconds is $16 t^{2}$ feet, and the speed of sound is 1120 feet per second, then the depth of the well is
(A) 784 feet.
(B) 342 feet.
(C) 1568 feet.
(D) 156.8 feet.
(E) None of the above.
(2nd American High School Mathematics Examination, 1951)

Your answer

Multiple choice: answer with the letter of the option you want.

Official solution

[Solution] Let the depth of the well be $h$ , and the time it takes for the stone to reach the bottom be $t$ , then $h=16 t^{2}$ . According to the problem, we have
$t+\frac{h}{1120}=7.7$ , which simplifies to $t^{2}+70 t-7 \cdot 77=0$ , yielding $t=7$ or -77 (discard the negative value). Therefore, the answer is $(A)$ .

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.