Question

1. at the middle school, the bell rings every 40 minutes to tell the students to change classes. across the street, the clock above city hall chimes every 30 minutes. both the school bell and the clock ring at noon. when will both bells ring at the same time again?

Explanation:

Step1: Encontrar MCM de 40 y 30

Primero, descomponemos en factores primos:
$40 = 2^3 \times 5$
$30 = 2 \times 3 \times 5$
El MCM se calcula tomando los exponentes máximos de cada factor primo:
$\text{MCM}(40,30) = 2^3 \times 3 \times 5 = 120$

Step2: Convertir minutos a horas

$120 \text{ minutos} = \frac{120}{60} = 2 \text{ horas}$

Step3: Sumar al tiempo inicial

Noon es 12:00, así que sumamos 2 horas:
$12:00 + 2:00 = 14:00$ (o 2:00 PM)

Answer:

Both bells will ring at the same time again at 2:00 PM (14:00).