Question

A staff gauge measures the height of the water level in a river compared to the average water level. At one gauge the river is 1 ft below its average water level of 10 ft. It begins to rise by a constant rate of 1.5 ft per hour.
Will the river reach a level of 7 ft above normal after 5 hours? Explain.

Answer 1

The river will not reach a level of 7 ft. after 5 hours.

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the initial value of y.

Let y represent the height of the water level after x hours.

Since the  river is 1 ft below its average water level and  begins to rise by a constant rate of 1.5 ft per hour. Hence:

b = -1, m = 1.5. The equation becomes:

y = 1.5x - 1

To reach a level of 7 ft. That is y = 7:

7 = 1.5x - 1

1.5x = 8

x = 5.3 hours

The river will not reach a level of 7 ft. after 5 hours.

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