Question

using the paths shown, how long is the shortest route from belmont to lancaster?
bloomington — 9.6 km — belmont — 11 km — norwood — 16.8 km — lancaster
norwood — 13.1 km — weston — 5.4 km — lancaster

Explanation:

Step1: Identify possible routes from Belmont to Lancaster.

First, the path from Belmont to Norwood is 11 km. Then from Norwood, we can go directly to Lancaster (16.8 km) or via Weston (13.1 km + 5.4 km). We need to calculate the lengths of these two possible routes from Belmont to Lancaster.

Step2: Calculate the length of the route via Weston.

The distance from Norwood to Weston is 13.1 km and from Weston to Lancaster is 5.4 km. So the total for this part (Norwood to Lancaster via Weston) is $13.1 + 5.4 = 18.5$ km. Then add the distance from Belmont to Norwood (11 km): $11 + 18.5 = 29.5$ km.

Step3: Calculate the length of the direct route from Norwood to Lancaster.

The distance from Belmont to Norwood is 11 km and from Norwood to Lancaster is 16.8 km. So the total is $11 + 16.8 = 27.8$ km.

Step4: Compare the two routes.

We have two route lengths: 29.5 km (via Weston) and 27.8 km (direct from Norwood to Lancaster). Since 27.8 < 29.5, the shortest route is 27.8 km.

Answer:

27.8