Choo Kheng must travel at least

Question

\[288\] kilometers in a submarine in order to reach her destination.
Let
\[S\] represent the number of hours the submarine can travel on the water's surface and
\[U\] represent the number of hours it can travel underwater in order to reach Choo Kheng's destination.
\[36S+64U \geq 288\]
The submarine travels for

\[2 \dfrac{2}{3}\] hours on the water's surface. What is the least number of hours the submarine must travel underwater in order for Choo Kheng to reach her destination?
Choose 1 answer:
Choose 1 answer:
(Choice A) The submarine must travel for at least
\[1\] hour.
A
The submarine must travel for at least
\[1\] hour.
(Choice B) The submarine must travel for at least
\[2\] hours.
B
The submarine must travel for at least
\[2\] hours.
(Choice C) The submarine must travel for at least
\[3\] hours.
C
The submarine must travel for at least
\[3\] hours.
(Choice D) The submarine must travel for at least
\[4\] hours.
D
The submarine must travel for at least
\[4\] hours.

Answer 1

To determine the least number of hours the submarine must travel underwater, we start with the inequality:

\[ 36S + 64U \geq 288 \]

We know that \(S\) (the hours traveled on the water's surface) is given as:

\[ S = 2 \frac{2}{3} \text{ hours} = \frac{8}{3} \text{ hours} \]

Now, we can substitute \(S\) into the inequality:

\[ 36 \left(\frac{8}{3}\right) + 64U \geq 288 \]

Calculating \(36 \times \frac{8}{3}\):

\[ 36 \times \frac{8}{3} = 12 \times 8 = 96 \]

Substituting this result back into the inequality gives:

\[ 96 + 64U \geq 288 \]

Now, we can isolate \(U\):

\[ 64U \geq 288 - 96 \] \[ 64U \geq 192 \] \[ U \geq \frac{192}{64} = 3 \]

Therefore, the least number of hours the submarine must travel underwater is:

\[ U \geq 3 \]

Thus, the correct choice is:

(Choice C) The submarine must travel for at least \(3\) hours.