Video: Finding the Real Distance given the Scale Ratio and the Drawing Distance

The distance between two cities on a map is 17 cm and the actual distance between them is 68 km. If the distance between two other cities on the same map is 15 cm, determine the real distance between them.

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Video Transcript

The distance between two cities on a map is 17 centimeters, and the actual distance between them is 68 kilometers. If the distance between two other cities on the same map is 15 centimeters, determine the real distance between them.

So let’s take the map distance compared to the real distance. Between the first set of cities, it was 17 centimeters on the map and 68 kilometers in real life. And between the second set of cities, there’s 15 centimeters on the map, but we don’t know the real distance between them. So we can call that 𝑥. And the way that we can solve this is to cross multiply. So we take 17 centimeters times 𝑥 kilometers and we get 17𝑥 centimeters kilometers. And then multiplying 68 times 15, we get 1020 centimeters kilometers.

And now to solve for 𝑥, we want 𝑥 in kilometers, so we wanna get rid of the 17 centimeters. So the 17 and the centimeters cancel. On the right, the centimeters cancel. And then 1020 divided by 17 is equal to 60 kilometers. So the number of kilometers for 𝑥 would be 60.

Therefore, the real distance between them will be 60 kilometers.

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