The water level of a river is below normal levels. Its water level is at 1 1/2

meters below sea
level. During the summer, the river drops another 2 1/3 meters below sea level. What is the water level at the end of summer? Remember, the elevation is below sea level. Account for
this in your answer.
The water level is __ meters from sea level

1 answer

To determine the water level at the end of summer, we first need to convert the fractions to improper fractions so we can easily add them together.

  1. The initial water level is \(1 \frac{1}{2}\) meters below sea level. Converting this to an improper fraction: \[ 1 \frac{1}{2} = \frac{2 \times 1 + 1}{2} = \frac{3}{2} \] So, the initial water level is \(-\frac{3}{2}\) meters (since it is below sea level).

  2. The additional drop in water level during summer is \(2 \frac{1}{3}\) meters. Converting this to an improper fraction: \[ 2 \frac{1}{3} = \frac{3 \times 2 + 1}{3} = \frac{7}{3} \] Therefore, the summer drop is \(-\frac{7}{3}\) meters.

  3. Now we can add these two values together to find the total water level at the end of summer: \[ -\frac{3}{2} - \frac{7}{3} \] To add these fractions, we need a common denominator. The least common multiple of 2 and 3 is 6.

    Converting \(-\frac{3}{2}\) to have a denominator of 6: \[ -\frac{3}{2} = -\frac{3 \times 3}{2 \times 3} = -\frac{9}{6} \]

    Converting \(-\frac{7}{3}\) to have a denominator of 6: \[ -\frac{7}{3} = -\frac{7 \times 2}{3 \times 2} = -\frac{14}{6} \]

  4. Now we add the two fractions: \[ -\frac{9}{6} - \frac{14}{6} = -\frac{9 + 14}{6} = -\frac{23}{6} \]

  5. The final water level at the end of summer is \(-\frac{23}{6}\) meters from sea level.

To express \(-\frac{23}{6}\) as a mixed number: \[ -\frac{23}{6} = -3 \frac{5}{6} \]

Thus, the water level is 3 5/6 meters below sea level.

So the answer is: The water level is 3.833... meters (or 3 5/6 meters) from sea level.