Scale Drawings

Part of the Decimals, Percents & Ratios section of Coddy's Pre-Algebra journey. Lesson 49 of 56.

A map is a drawing at a scale: on this map, 1 cm stands for 20 km on the ground. A scale is a rate, 20 km per cm. Two towns are 4 cm apart on the map, so the real distance is 4 × 20, which is 80 km.

Why multiply? Every centimetre on the map is a whole 20 km on the ground, so 4 cm is four lots of 20 km. It is the same as speed: every hour adds the same distance, and here every centimetre does.

Going the other way divides. A real distance of 60 km takes 60 / 20, which is 3 cm on the map. Floor plans work the same way: if 1 cm stands for 2 m, a room drawn 5 cm long is 10 m long.

Challenge

On a map, 1 cm stands for 25 km. Two cities are 7 cm apart on the map. Find the real distance k between them, in km. Write k equal to the calculation, then work it out on the next line.