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QuestionWhat is the distance between two towns on a map if 2 cm2 \mathrm{~cm} equals 30mi30 \mathrm{mi} and the actual distance is 75mi75 \mathrm{mi}?

Studdy Solution

STEP 1

Assumptions1. On the map, cm represents30 miles. . The actual distance between the two towns is75 miles.
3. The scale factor is constant across the map.

STEP 2

First, we need to find the scale factor of the map. We can do this by dividing the actual distance by the map distance.
Scale factor=Actual distanceMap distanceScale\, factor = \frac{Actual\, distance}{Map\, distance}

STEP 3

Now, plug in the given values for the actual distance and map distance to calculate the scale factor.
Scale factor=30 mi2 cmScale\, factor = \frac{30\, mi}{2\, cm}

STEP 4

Calculate the scale factor.
Scale factor=30 mi2 cm=15 mi/cmScale\, factor = \frac{30\, mi}{2\, cm} =15\, mi/cm

STEP 5

Now that we have the scale factor, we can find the map distance between the two towns. This can be done by dividing the actual distance by the scale factor.
Map distance=Actual distanceScale factorMap\, distance = \frac{Actual\, distance}{Scale\, factor}

STEP 6

Plug in the values for the actual distance and the scale factor to calculate the map distance.
Map distance=75 mi15 mi/cmMap\, distance = \frac{75\, mi}{15\, mi/cm}

STEP 7

Calculate the map distance.
Map distance=75 mi15 mi/cm=5 cmMap\, distance = \frac{75\, mi}{15\, mi/cm} =5\, cmThe distance between the towns on the map is5 cm.

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