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36 S+64 U >= 288 Choo Kheng must travel at least 288 kilometers in a submarine in order to reach her destination. The submarine travels at a constant speed on the water's surface, and travels at a constant speed underwater. In the given inequality, S represents the number of hours the submarine can travel on the water's surface and U represents the number of hours it can travel underwater in order to reach Choo Kheng's destination. If the submarine travels for 2(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?

36S+64U≥288 36 S+64 U \geq 288 \newlineChoo Kheng must travel at least 288288 kilometers in a submarine in order to reach her destination. The submarine travels at a constant speed on the water's surface, and travels at a constant speed underwater. In the given inequality, S S represents the number of hours the submarine can travel on the water's surface and U U represents the number of hours it can travel underwater in order to reach Choo \mathrm{Choo} Kheng's destination. If the submarine travels for 223 2 \frac{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?

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Q. 36S+64U≥288 36 S+64 U \geq 288 \newlineChoo Kheng must travel at least 288288 kilometers in a submarine in order to reach her destination. The submarine travels at a constant speed on the water's surface, and travels at a constant speed underwater. In the given inequality, S S represents the number of hours the submarine can travel on the water's surface and U U represents the number of hours it can travel underwater in order to reach Choo \mathrm{Choo} Kheng's destination. If the submarine travels for 223 2 \frac{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?
  1. Understand Inequality Representation: Understand the given inequality and what it represents.\newlineThe inequality 36S+64U≥28836S + 64U \geq 288 represents the total distance traveled by the submarine, where SS is the number of hours on the surface and UU is the number of hours underwater. The submarine must travel at least 288288 kilometers to reach the destination.
  2. Convert Mixed Number to Improper Fraction: Convert the mixed number 2232\frac{2}{3} hours into an improper fraction to make calculations easier.\newline2232\frac{2}{3} hours = 2×3+23\frac{2 \times 3 + 2}{3} = 83\frac{8}{3} hours
  3. Substitute Value of S: Substitute the value of SS in the inequality with 83\frac{8}{3} hours.\newline36S+64U≥28836S + 64U \geq 288 becomes 36×(83)+64U≥28836 \times \left(\frac{8}{3}\right) + 64U \geq 288.
  4. Perform Surface Distance Calculation: Perform the multiplication to find the distance traveled on the surface.\newline36×(83)=12×8=9636 \times \left(\frac{8}{3}\right) = 12 \times 8 = 96\newlineSo, the inequality now is 96+64U≥28896 + 64U \geq 288.
  5. Solve for U: Subtract 9696 from both sides of the inequality to solve for UU. \newline64U≥288−9664U \geq 288 - 96 \newline64U≥19264U \geq 192
  6. Find Minimum Hours U: Divide both sides of the inequality by 6464 to find the minimum hours UU.\newlineU≥19264U \geq \frac{192}{64}\newlineU≥3U \geq 3

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