a walk up a hill starts at a car park on the 100m contour and climbs steadily to a summet at 240m. on a map with scale 1:25000 the distance along the path from the car park to the summet is 9.6cm.

how long it will to reach su,,it and back according to Naismith's rule.

Naismith's rule provides a rough estimate of the time required to complete a hike based on the distance traveled and the ascent involved. It assumes an average walking speed of 4 kilometers per hour (or 1 kilometer every 15 minutes) on level ground, with additional time allowances for uphill sections.

To use Naismith's rule, we need to determine the total ascent and descent involved in the hike, as well as the distance traveled. Let's calculate that step by step:

1. Determine the total ascent: The hike starts at the car park at the 100m contour and climbs to the summit at 240m. The total ascent is therefore 240m - 100m = 140 meters.

2. Calculate the distance traveled: Given that the distance on the map between the car park and the summit is 9.6cm, and the map scale is 1:25000, we can calculate the equivalent distance in kilometers.

Convert the map scale to a ratio: 1cm on the map represents 25000cm in reality.
Convert centimeters to kilometers: 9.6cm * (25000cm/100000cm) = 2.4 kilometers.

So the distance traveled from the car park to the summit is 2.4 kilometers.

3. Calculate the time for ascent: Naismith's rule allows 1 minute for every 10 meters of ascent. So, for the 140 meters of ascent, we can estimate the time required as 140 meters / 10 meters per minute = 14 minutes.

4. Calculate the time for the distance traveled: Naismith's rule assumes a walking speed of 1 kilometer every 15 minutes (4 kilometers per hour). Since we already determined the distance traveled to be 2.4 kilometers, we can estimate the time based on this speed: 2.4 kilometers * 15 minutes per kilometer = 36 minutes.

5. Calculate the total time: To get the total time required, we sum the time for ascent (14 minutes) and the time for the distance traveled (36 minutes): 14 minutes + 36 minutes = 50 minutes.

Thus, according to Naismith's rule, it is estimated to take approximately 50 minutes to reach the summit. To determine the time required for the round trip, you would double this estimate, resulting in a total of 100 minutes or 1 hour and 40 minutes.