Question

A fish is swimming at −5.4 meters, or 5.4 meters below sea level. Every 2 minutes it descends another 1.5 meters. How long will it take for the fish to reach a depth of −37.8 meters?

Answer 1

The fish starts at a depth of -5.4 meters and needs to reach -37.8 meters. First, we need to calculate the total depth the fish needs to descend:

\[
-37.8 \text{ meters} - (-5.4 \text{ meters}) = -37.8 + 5.4 = -32.4 \text{ meters}
\]

The fish needs to descend a total of 32.4 meters.

Next, we know that the fish descends 1.5 meters every 2 minutes. To find out how many 1.5-meter increments are needed to reach the total descent of 32.4 meters, we divide the total descent by the descent per interval:

\[
\frac{32.4 \text{ meters}}{1.5 \text{ meters}} = 21.6
\]

Since the fish can only descend in whole increments of 1.5 meters, we round this up to 22 intervals.

Now we find out the total time taken for these 22 increments:

\[
22 \text{ intervals} \times 2 \text{ minutes/interval} = 44 \text{ minutes}
\]

Therefore, it will take the fish **44 minutes** to reach a depth of -37.8 meters.