Question

A MIR submersible is a type of submarine. As a MIR dives, its elevation changes by 100 feet each minute.

a. From the surface, a MIR takes about 200 minutes to reach the lowest point to which it can dive. What is its elevation at that point?

b. How long would a MIR take to dive to 1000 feet below sea level?

Short answer

a. The elevation at the lowest point after 200 minutes is $-20000\text{feet}$.

b. It would take 10 minutes for MIR to dive 1000 feet below the sea level.

Step-by-step solution

Step-1 – Apply the concept of product

In mathematics, a product is the result of multiplication, or an expression that identifies factors to be multiplied. The numbers that are being multiplied are called the factors and the product of two numbers is the result you get when you multiply them together.

Step-2 – Rule and examples of multiplication of integers 

Multiplication of Integers

RULE 1: The product of a positive integer and a negative integer is negative.

RULE 2: The product of two positive integers is positive.

RULE 3: The product of two negative integers is positive.

Type of Numbers	Result	Example
Positive x Positive	Positive	1 x 5 = 5
Negative x Negative	Positive	(– 1) x (– 5) = 5
Positive x Negative	Negative	1 x (– 5) = – 5
Negative x Positive	Negative	( – 1) x 5 = – 5

From the surface, a MIR takes about 200 minutes to reach the lowest point to which it can dive. What is its elevation at that point?

Given in the question:

MIR takes about 200 minutes to reach lowest point to which it can dive.

Since, as a MIR dives its elevation changes by – 100 feet each minute.

Therefore, in 200 minutes the elevation at the lowest point is

– 100 (200) = – 20000 feet

Thus, the elevation at the lowest point is – 20000 feet.

b.Step-1 – The concept of quotient

In mathematics, the quotient is the number obtained by dividing one number by another number.

Step-2 – Rules and examples of division of integers

Rules and example of Division of integers

RULE 1: The quotient of a positive integer and a negative integer is negative.

RULE 2: The quotient of two positive integers is positive.

RULE 3: The quotient of two negative integers is positive.

Examples:

Rule 1: (– 8) ÷ (+ 4) = – 2

Rule 2: (+ 6) ÷ (– 3) = – 2

Rule 3: (+ 9) ÷ (+ 3) = +3

Rule 4: (– 6) ÷ (– 2) = +3

Step-3 – How long would a MIR take to dive to 1000 feet below sea level?

According to the question:

The elevation of MIR changes by $-100$ feet each minute.

Since, as a MIR dives its elevation changes by – 100feet each minute.

Rule: The quotient of two negative integers is positive.

Time taken by MIR to dive to 1000 feet below the sea level is the quotient of –1000 by – 100. Therefore,

$\frac{-1000}{-100}=10\text{minutes}$.

Thus, it would take 10 minutes for MIR to dive 1000 feet below the sea level.