Question

Tres empresas de transporte terrestre cumplen el recorrido Lima - Piura, siendo la longitud del trayecto de aproximadamente 1 000 km. La frecuencia de salida es de 10, 12 y 15 días, respectivamente. Si el 14 de marzo tuvieron una partida simultánea, ¿cuántas veces vuelven a coincidir en su partida hasta el 31 de julio?

A)1 B) 2 C) 3 D) 4

Answer 1

B) 2

Explanation:

We have to find the interval of time for which they begin the traject simultaneously.

One begins each 10 days, other each 12 and other each 15. So to find the number of days before dey start together, we have to find the lesser common multiple(non-zero) between 10,12, and 15.

M(10) = {0,10,20,30,40,50,60,...}

M(10) are the multiples of 10.

M(12) = {0,12,24,36,48,60,...}

M(15) = {0,15,30,45,60,...}

So the lesser common multiple between 10,12 and 15 is 60.

This means that they will begin together each 60 days.

So, first on March 14, after that:

60 days is approximately months.

So approxiately on May 14, and then approximately on July 14

That is, two times before July 31.

So the correct answer is:

B) 2