The water level of the 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 the summer remember the elevation is below sea level account for this in your answer

1 answer

To find the water level of the river at the end of summer, we need to add the two decreases in elevation below sea level.

  1. The water level is initially at \(1 \frac{1}{2}\) meters below sea level, which we can convert to an improper fraction: \[ 1 \frac{1}{2} = \frac{3}{2} \text{ meters below sea level} \]

  2. During the summer, the water level drops another \(2 \frac{1}{3}\) meters below sea level, which we also convert to an improper fraction: \[ 2 \frac{1}{3} = \frac{7}{3} \text{ meters below sea level} \]

Now, we need to add these two values together. To do this, we first need a common denominator. The least common multiple of \(2\) and \(3\) is \(6\).

Now, we convert both fractions:

  • For \(\frac{3}{2}\): \[ \frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6} \]

  • For \(\frac{7}{3}\): \[ \frac{7}{3} = \frac{7 \times 2}{3 \times 2} = \frac{14}{6} \]

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

Thus, the water level at the end of summer is \(\frac{23}{6}\) meters below sea level. To express this as a mixed number, we can do the division: \[ \frac{23}{6} = 3 \frac{5}{6} \]

So, the water level at the end of summer is \(3 \frac{5}{6}\) meters below sea level.