A walk up a hill starts at a car park on the 100m contour and climbs steadily to a summit at 240 m. On a map with scale 1:25 000 the distance along the path from the car park to the summit is 9.6 cm.

Choose the three true statements from the following.
Options
A) The distance on the ground from the car park to the summit is about
2.4 km.
B) The distance on the ground from the car park to the summit is about
4.2 km.
C) The average mathematical gradient of the climb is 0.058 (to 2 s.f.).
D) The average mathematical gradient of the climb is 0.17 (to 2 s.f.).
E) Naismith’s rule predicts that the walk to the summit and back down
to the car park will take about 40 minutes.
F )Naismith’s rule predicts that the walk to the summit and back down to the car park will take about 1 hour 10 minutes.
G) Naismith’s rule predicts that the walk to the summit and back down to the car park will take about 1 hour 30 minutes

To determine which statements are true, we need to use the information given and perform some calculations.

1. We know that the distance on the map from the car park to the summit is 9.6 cm.
2. The map scale is 1:25,000, which means that 1 cm on the map represents 25,000 cm (or 250 meters) on the ground.
3. To find the distance on the ground from the car park to the summit, we multiply the distance on the map by the scale factor: 9.6 cm * 250 meters/cm = 2400 meters or 2.4 km.

Therefore, statement A) The distance on the ground from the car park to the summit is about 2.4 km is true.

Next, let's calculate the average mathematical gradient of the climb.

1. The climb starts at the car park on the 100m contour and reaches a summit at 240m, giving a total height gain of 240m - 100m = 140m.
2. The distance on the ground from the car park to the summit is 2.4 km.
3. To calculate the average mathematical gradient, we divide the height gain (140m) by the distance (2.4 km), and then round to 2 significant figures: 140m / 2.4 km = 0.058 (rounded to 2 decimal places).

Therefore, statement C) The average mathematical gradient of the climb is 0.058 (to 2 s.f.) is true.

Lastly, let's consider Naismith's rule for estimating walking times.

1. Naismith's rule suggests that for every 1000 ft (or roughly 300 meters) of vertical ascent, one should add 1 hour to the estimated walking time.
2. The climb from the car park to the summit has a height gain of 140m, which is roughly 460 ft.
3. According to Naismith's rule, we would add 1 hour to the estimated walking time for this ascent.

Therefore, statement E) Naismith’s rule predicts that the walk to the summit and back down to the car park will take about 40 minutes is false.

Based on the given information and calculations, the three true statements are:

A) The distance on the ground from the car park to the summit is about 2.4 km.
C) The average mathematical gradient of the climb is 0.058 (to 2 s.f.).
F) Naismith’s rule predicts that the walk to the summit and back down to the car park will take about 1 hour 10 minutes.

9.6 cm * 10^-2 m /cm = 9.6*10^-2 m

9.6*10^-2 * 25,000 = 2,400m
which is 2.4 km (answer A)

240 - 100 = 140 meters up
140/2400 = .058 (answer C)

I have no idea what Naismith's rule is, use Google