Mr. Dyer is studying a map. The map has a scale that says 1.5 inches is equivalent to 125 miles. Mr. Dyer measures and sees that two cities are half a foot apart. He has enough gas in his truck to travel 580 miles. Can he make it from one city to the other on the gas in his truck?

Yes he can make the trip without having to refuel.

The distance between the two cities is 500 miles.

Work Shown:

half a foot = 1/2 ft = (1/2)*(12 inches) = 6 inches

Based on the scale given, we can say,

(map length)/(real length) = (map length)/(real length)

(1.5 inches)/(125 miles) = (6 inches)/(x miles)

1.5/125 = 6/x

1.5x = 125*6 cross multiply

1.5x = 750

x = 750/1.5 divide both sides by 1.5

x = 500

The two cities are 500 miles apart. Since this is less than 580, he can make the trip without having to refuel.

This is assuming he drives directly from the first city to the second, without any additional pitstops or detours. Though in reality, straight line distance on a map doesn't always necessarily correspond to the road distance traveled (since the road tends to wind or curve often). However, for the sake of this problem, we'll just assume the road is a straight line to keep things simple.

Another approach:

1.5 inches = 125 miles

3 inches = 250 miles multiply both sides by 2

6 inches = 500 miles multiply both sides by 2

half a foot = 500 miles

So half a foot on paper corresponds to 500 miles in real life.