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Dante commutes to work 4 mornings a week. For his commute each morning, he walks for 10 minutes, waits and rides the bus for x minutes, and waits and rides the train for y minutes. If Dante spends at least 3.5 hours on his morning commute each week, which of the following inequalities best describes Dante's weekly morning commute? Choose 1 answer: (A) x+y+10 >= 3.5(60) (B) x+y+10 >= 3.5(60)(4) (c) 4(x+y)+10 >= 3.5(60) (D) 4(x+y+10) >= 3.5(60)

Dante commutes to work 44 mornings a week. For his commute each morning, he walks for 1010 minutes, waits and rides the bus for x x minutes, and waits and rides the train for y y minutes. If Dante spends at least 33.55 hours on his morning commute each week, which of the following inequalities best describes Dante's weekly morning commute?\newlineChoose 11 answer:\newline(A) x+y+10≥3.5(60) x+y+10 \geq 3.5(60) \newline(B) x+y+10≥3.5(60)(4) x+y+10 \geq 3.5(60)(4) \newline(C) 4(x+y)+10≥3.5(60) 4(x+y)+10 \geq 3.5(60) \newline(D) 4(x+y+10)≥3.5(60) 4(x+y+10) \geq 3.5(60)

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Q. Dante commutes to work 44 mornings a week. For his commute each morning, he walks for 1010 minutes, waits and rides the bus for x x minutes, and waits and rides the train for y y minutes. If Dante spends at least 33.55 hours on his morning commute each week, which of the following inequalities best describes Dante's weekly morning commute?\newlineChoose 11 answer:\newline(A) x+y+10≥3.5(60) x+y+10 \geq 3.5(60) \newline(B) x+y+10≥3.5(60)(4) x+y+10 \geq 3.5(60)(4) \newline(C) 4(x+y)+10≥3.5(60) 4(x+y)+10 \geq 3.5(60) \newline(D) 4(x+y+10)≥3.5(60) 4(x+y+10) \geq 3.5(60)
  1. Rephrase Question: First, let's rephrase the ＂What inequality best describes Dante's weekly morning commute time in minutes, given that he commutes 44 mornings a week and spends at least 3.53.5 hours on his commute?＂
  2. Breakdown of Commute: Dante's weekly commute consists of walking, waiting and riding the bus, and waiting and riding the train. Each morning, this amounts to 1010 minutes of walking, xx minutes on the bus, and yy minutes on the train. Since he commutes 44 mornings a week, the total weekly time spent walking is 4×104 \times 10 minutes.
  3. Convert Hours to Minutes: To convert the 3.53.5 hours into minutes, we multiply by 6060, since there are 6060 minutes in an hour. This gives us 3.5×603.5 \times 60 minutes.
  4. Express Total Time: Now, we need to express the total weekly commute time in terms of xx and yy. Since Dante commutes 44 mornings a week, the total time spent on the bus and train each week is 4x+4y4x + 4y minutes.
  5. Formulate Inequality: Adding the time spent walking to the time spent on the bus and train gives us the total weekly commute time: 4x+4y+4×104x + 4y + 4 \times 10 minutes.
  6. Simplify Inequality: Since Dante spends at least 3.53.5 hours on his commute each week, the inequality must reflect that the total weekly commute time is greater than or equal to 3.5×603.5 \times 60 minutes. Therefore, the inequality is 4x+4y+40≥3.5×604x + 4y + 40 \geq 3.5 \times 60.
  7. Match with Answer: Simplifying the inequality by factoring out the 44 from the left side, we get 4(x+y+10)≥3.5×604(x + y + 10) \geq 3.5 \times 60.Comparing the simplified inequality with the answer choices, we find that it matches option (D): 4(x+y+10)≥3.5×604(x + y + 10) \geq 3.5 \times 60.

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