A hiker stands at an elevation of [tex]-89 \frac{1}{5}[/tex] meters below sea level, and his brother stands at an elevation of [tex]\frac{48}{56}[/tex] meters above sea level. What is the distance between the two brothers?

a) [tex]89 \frac{9}{5}[/tex] meters
b) [tex]89 \frac{1}{5}[/tex] meters
c) [tex]89 \frac{7}{5}[/tex] meters
d) [tex]89 \frac{8}{5}[/tex] meters

To find the distance between the hiker and his brother, we need to calculate the total vertical separation between them. The hiker stands at an elevation of -89 1/5 meters below sea level, which can be expressed as -89.2 meters. His brother stands at an elevation of 48/56 meters above sea level, which simplifies to 6/7 meters.

Now, we'll calculate the total separation by adding these two values:

-89.2 meters (hiker's elevation) + 6/7 meters (brother's elevation) = -89.2 + 6/7 meters

To add these two values, we need a common denominator, which is 7. So, we'll convert -89.2 to have a denominator of 7:

-89.2 = -89 1/5 = -89 14/7 = -89 2/7 meters

Now, we can add the elevations:

-89 2/7 meters + 6/7 meters = -89 8/7 meters

To simplify, we can express this as a mixed number:

-89 8/7 meters = -89 1/7 meters

Now, the distance between the two brothers is 89 1/7 meters. This can be further simplified to 89 1/5 meters, which is our final answer.

Option b is correct.

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