Multiple choice

Directions: Compare the two quantities in A and B. A boat traveled upstream a distance of 90 miles at an average speed of (V - 3) miles per hour and then traveled the same distance downstream at an average of (V + 3) miles per hour. If the trip upstream took half an hour longer than the trip downstream. x = Hours did it take the boat to travel downstreamy = Hours did it take the boat to travel upstream Quantity A Quantity B 6x 5y

  1. Quantity A is greater than quantity B.

  2. Quantity B is greater than quantity A.

  3. Both quantities are equal.

  4. The relationship between the quantities cannot be determined.
Reveal answer Fill a bubble to check yourself
C Correct answer
AI explanation

The downstream time x is 90 / (V + 3) and the upstream time y is 90 / (V - 3). Setting the difference to half an hour yields the equation 90 / (V - 3) - 90 / (V + 3) = 0.5, which simplifies to 540 = 0.5(V^2 - 9) and gives V = 33 mph. Substituting V gives x = 90 / 36 = 2.5 hours and y = 90 / 30 = 3 hours. Comparing the quantities, 6x is 6 * 2.5 = 15 and 5y is 5 * 3 = 15, showing they are identical. The result is that both quantities are equal.

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