Question

Jim is driving to Denver. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Jim has 61 miles to his destination after 41 minutes of driving, and he has 42.3 miles to his destination after 63 minutes of driving. How many miles will he have to his destination after 81 minutes of driving

Answer 1

Jim has to travel 26.82 miles more to reach Denver.

What is the equation of a line?

Let the first point be = (x₁ , y₁)

Let the second point be = (x₂ , y₂)

m(slope) = (y₂ - y₁) / (x₂ - x₁)

Equation of line = (y - y₁) = m(x - x₁)

Let the no. of miles be plotted on X-axis

Let the driving time be plotted on Y-axis

First point = (61 , 41)

Second point = (42.3 , 63)

Slope of the linear function = (63 - 41)/(42.3 - 61) = -1.17

Equation of the line = (y - 41) = -1.17(x - 61)

Given time of driving = 81 min

Number of miles = (81 - 41) = -1.17(x - 61)

40/-1.17 = x - 61

-34.18 + 61 = x

x = 26.82

Hence, Jim has to travel 26.82 miles more to reach Denver.

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