College

The sea floor is 104 feet below sea level. Katy is 28 feet below sea level and is moving downward at a rate of 4 feet per minute.

Colin used the following calculation to determine how long it will take Katy to reach the sea floor:

[tex]104 - 28 \div 4 = 97 \text{ minutes}[/tex]

Is he correct? Explain.

Answer :

To determine the time it takes for Katy to reach the sea floor, we first find the total distance she needs to travel. The sea floor is at [tex]$104$[/tex] feet below sea level, and Katy is at [tex]$28$[/tex] feet below sea level. Therefore, the distance is

[tex]$$
104 - 28 = 76 \text{ feet}.
$$[/tex]

Since Katy is moving downward at a rate of [tex]$4$[/tex] feet per minute, the time required to travel this distance is given by

[tex]$$
\text{Time} = \frac{\text{Distance}}{\text{Rate}} = \frac{76}{4} = 19 \text{ minutes}.
$$[/tex]

Colin's calculation,

[tex]$$
104 - \frac{28}{4} = 104 - 7 = 97 \text{ minutes},
$$[/tex]

is incorrect because it applies the division operation to [tex]$28$[/tex] before performing the subtraction. The correct approach is to subtract first and then divide, as shown above.

Thus, the correct time for Katy to reach the sea floor is [tex]$19$[/tex] minutes.