Choosing Units and Scale on a Map Task
A class is planning a walking excursion. On a map with a scale of 1:10 000, the route from school to the museum measures 7.5 cm. The route from the museum to the park measures 4.2 cm. The class walks at about 4 km per hour and plans a 20-minute stop at the museum. The teacher says the group must be back at school within 3 hours. A student measures the return route as 6.8 cm on the same map.
1. Convert the map measurements to real distances in metres and kilometres.
Read the worked answer
Scale 1:10 000 means 1 cm on the map = 10 000 cm in real life = 100 m.
School to museum: 7.5 cm × 100 m = 750 m = 0.75 km. Museum to park: 4.2 cm × 100 m = 420 m = 0.42 km. Return route: 6.8 cm × 100 m = 680 m = 0.68 km.
A common error is to treat 1:10 000 as 1 cm = 10 000 m, which would give 75 km. Checking that 10 000 cm = 100 m prevents that mistake.
2. Work out the total walking time and decide whether the trip fits within 3 hours.
Read the worked answer
Total distance = 0.75 + 0.42 + 0.68 = 1.85 km.
Time walking = distance ÷ speed = 1.85 km ÷ 4 km/h = 0.4625 hours. Convert: 0.4625 × 60 = 27.75 minutes, about 28 minutes.
Add the 20-minute museum stop: 28 + 20 = 48 minutes.
This is well within 3 hours (180 minutes), leaving about 132 minutes spare. Even allowing for slower walking (say 3 km/h gives 1.85 ÷ 3 = 0.617 h ≈ 37 minutes), the trip still fits comfortably. The judgement is to convert units consistently and to add the stop time, which students often forget.
3. The teacher wants a safety margin of 30 minutes. How much extra distance could the class add at 4 km/h and still keep the margin?
Read the worked answer
Time used so far = 48 minutes. Budget with margin = 180 − 30 = 150 minutes. Spare time = 150 − 48 = 102 minutes = 1.7 hours.
Extra distance possible = speed × time = 4 km/h × 1.7 h = 6.8 km.
So the class could add up to 6.8 km of walking and still return within the margin. In map terms, 6.8 km = 6800 m ÷ 100 m per cm = 68 cm on the map, which is far more than the planned route, so the plan is safe. The key step is converting the spare minutes to hours before multiplying by the speed.