The rate at which Catlin runs can be determined from the graph by finding the coordinates of a grid point that lies on the line. The line goes through the origin, so the relationship between time and distance is proportional.

We see that the point (miles, minutes) = (1 2/3, 12) lies on the graph, so the contant of proportionality is ...

k = y/x = 12/(5/3) = 36/5 = 7.2 . . . . minutes/mile

The proportion can be written ...

distance/(20 minutes) = (1 mile)/(7.2 minutes)

distance = (20/7.2) miles = 2 7/9 miles

Catlin will run 2 7/9 miles in 20 minutes

The proportion can be written ...

time/(3 miles) = (7.2 minutes)/(1 mile)

time = (3)(7.2 minutes) = 21.6 minutes

Catlin was running 21.6 minutes

In 1 hour, Catlin will run 3 times as far as in 20 minutes. Using the result from part A, we find ...

3(2 7/9 miles) = 8 1/3 miles 8 1/3 miles

Catlin will run 8 1/3 miles in one hour.

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<em>Additional comment</em>

Once we have a relationship between minutes and miles, we can write proportions with either of those numbers in the numerator or denominator. We find it convenient to put the unknown value in the numerator of a proportion, which is why the ratios are written differently in the different parts of the problem.

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2 years ago