Question

chaya has a map that shows the lengths of some hiking trails. the scale is shown in the drawing.
what number can you multiply each distance in the scale drawing by to find the actual distance?
0.5
what is the actual length of the waterfall trail?
km
(chart: waterfall ---6 cm--- parking ---9 cm--- picnic area; parking ---3 cm--- ranger tower; scale 3 cm : 1.5 km)

Explanation:

First Sub - Question (What number to multiply)

Step1: Analyze the scale

The scale is given as \(3\space\text{cm}:1.5\space\text{km}\). To find the multiplier, we calculate the actual distance per centimeter.
We know that for \(3\space\text{cm}\) on the map, the actual distance is \(1.5\space\text{km}\). So, the multiplier (actual distance per centimeter) is \(\frac{1.5}{3}\).

Step2: Calculate the multiplier

\(\frac{1.5}{3}= 0.5\) (Wait, no, wait. Wait, the scale is \(3\space\text{cm}\) represents \(1.5\space\text{km}\), so to find how much \(1\space\text{cm}\) represents, we do \(1.5\div3 = 0.5\space\text{km per cm}\). But the first sub - question is "What number can you multiply each distance in the scale drawing by to find the actual distance?". Wait, maybe I misread. Wait, the scale is \(3\space\text{cm}:1.5\space\text{km}\), so if we let \(x\) be the number we multiply the map distance (in cm) by to get actual distance (in km), then for a map distance \(d\) (in cm), actual distance \(D\) (in km) is \(D=d\times x\). From the scale, when \(d = 3\), \(D = 1.5\), so \(x=\frac{1.5}{3}=0.5\)? Wait, no, wait \(3\space\text{cm}\) is \(1.5\space\text{km}\), so \(1\space\text{cm}\) is \(0.5\space\text{km}\), so the multiplier is \(0.5\) (km per cm). But wait, maybe the first sub - question's answer is \(0.5\) (as given in the gray box, maybe it's a fill - in - the - blank and we need to confirm). But let's move to the second sub - question.

Second Sub - Question (Actual length of waterfall trail)

Step1: Identify the map distance of waterfall trail

From the map, the distance from Waterfall to Parking is \(6\space\text{cm}\).

Step2: Use the multiplier

We know that the multiplier (from the first sub - question or from the scale) is \(0.5\space\text{km per cm}\) (since \(3\space\text{cm}\) corresponds to \(1.5\space\text{km}\), so \(1\space\text{cm}\) corresponds to \(1.5\div3 = 0.5\space\text{km}\)). So, to find the actual length, we multiply the map distance (\(6\space\text{cm}\)) by the multiplier (\(0.5\space\text{km/cm}\)).
The formula for actual length \(L\) is \(L=\text{map distance}\times\text{multiplier}\).

Step3: Calculate the actual length

\(L = 6\times0.5=3\space\text{km}\)

Answer:

s:

• For the first sub - question: The number is \(0.5\) (km per cm, so when you multiply the distance in the scale drawing (in cm) by \(0.5\), you get the actual distance in km).
• For the second sub - question: The actual length of the waterfall trail is \(3\space\text{km}\).