Question

A submarine is only allowed to change its depth by rising toward the surface in 60-meter stages. It starts at -340 meters. How many stages will it take to return to the surface?

Answer 1

Answer: 6 stages

Explanation

-340 = starting depth

n = number of stages

60n = total vertical displacement, i.e. how much you move up

-340+60n = final depth after moving n stages (each stage 60 meters)

Set this equal to zero and solve for n.

-340+60n = 0

60n = 340

n = 340/60

n = 5.667 approximately

n = 6 is the final answer

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If 5 stages were done, then the depth would be

-340+60n = -340+60*5 = -40

Meaning that you would still be underwater at a depth of 40 meters below the surface.

If 6 stages are done, then,

-340+60n = -340+60*6 = 20

At this point the depth is 20 meters above the surface. Of course the submarine cannot hover or fly. So at this point we would set the depth to 0 instead.

This shows that 5 stages aren't enough, but 6 stages are enough to return to the surface. The last stage will cover 40 meters instead of 60 meters.

So this is why we round the n = 5.667 to n = 6

Answer 2

6

Explanation:

340/60 = 5.6 recurring. it would be 6 stages becasue it can't do half a stage, and if it was 5 stages it would still be underwater.