a group of nine marine scientists is exploring an underwater cave five hundred eighty - eight meters below…

a group of nine marine scientists is exploring an underwater cave five hundred eighty - eight meters below the surface in macedonia. the scientists work below the surface in eight - hour shifts. they travel up and down in a pair of diving bells, and each holds three people. when one crew is coming up, the other is being lowered at the same time. the diving bells can be lowered at the rate of twenty - one meters per minute but can be raised at the rate of only seven meters per minute. assume that both diving bells start at the same time and that distances above sea level are positive ones. one of the values you will find in the worksheet below will not make sense in reality. for an extra challenge, you may consider on your own which one it is and why it does not make sense outside of the algebraic model.\n\ndefine units for the time, the depth of the diving bell going down, and the depth of the diving bell coming up. enter a variable for the time and use this variable to write expressions for the depth of the diving bell going down and the depth of the diving bell coming up.\n\n1. what is the depth of each bell after 18 minutes?

a group of nine marine scientists is exploring an underwater cave five hundred eighty - eight meters below the surface in macedonia. the scientists work below the surface in eight - hour shifts. they travel up and down in a pair of diving bells, and each holds three people. when one crew is coming up, the other is being lowered at the same time. the diving bells can be lowered at the rate of twenty - one meters per minute but can be raised at the rate of only seven meters per minute. assume that both diving bells start at the same time and that distances above sea level are positive ones. one of the values you will find in the worksheet below will not make sense in reality. for an extra challenge, you may consider on your own which one it is and why it does not make sense outside of the algebraic model.\n\ndefine units for the time, the depth of the diving bell going down, and the depth of the diving bell coming up. enter a variable for the time and use this variable to write expressions for the depth of the diving bell going down and the depth of the diving bell coming up.\n\n1. what is the depth of each bell after 18 minutes?

Answer

Explanation:

Step1: Definir fórmula para la campana que desciende

La velocidad de descenso es de 21 metros por minuto. Sea $t$ el tiempo en minutos. La expresión para la profundidad $d_{descenso}$ de la campana que desciende es $d_{descenso}=- 21t$ (negativo porque es hacia abajo).

Step2: Definir fórmula para la campana que sube

La velocidad de ascenso es de 7 metros por minuto. La expresión para la profundidad $d_{ascenso}$ de la campana que sube es $d_{ascenso}=-588 + 7t$ (empezan a 588 metros de profundidad, por lo que se resta ese valor inicial y luego se suma la distancia recorrida hacia arriba).

Step3: Calcular la profundidad de la campana que desciende después de 18 minutos

Sustituir $t = 18$ en $d_{descenso}=-21t$. $d_{descenso}=-21\times18=-378$ metros.

Step4: Calcular la profundidad de la campana que sube después de 18 minutos

Sustituir $t = 18$ en $d_{ascenso}=-588 + 7t$. $d_{ascenso}=-588+7\times18=-588 + 126=-462$ metros.

Answer:

La profundidad de la campana que desciende después de 18 minutos es - 378 metros y la profundidad de la campana que sube después de 18 minutos es - 462 metros.