an express bus travels directly from A-town to B-ville. A local bus also links these two towns, but it....?

Question

goes west 30 km from A-town to C-city, then 30 km south to D-burg, 12km west to E-town and 30 km N<45>E to B-Ville.

a) what is the shortest distance from A-town to B-ville?


b) if the express but takes 0.45 hours to go from A-town to B-ville, and the local bus takes 3.0 hour, calculate the average velocity for each bus.


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Answer 1

a)
Find N - S and E - W separately:
A ------> B (N - S):
-30 + 30cos45 = -8.7868km
A ------> B(E - W):
-30 - 12 +30sin45 = -20.7868km
Use the Pythagorean theorem:
D = √[(-8.7868)^2 + (-20.7868)^2] = 22.5677KM
Average velocity = Displacement/total time
V(express) = 22.5677/.45 = 50.15km/hr
V(local) = 22.5677/3.0 = 7.523km/hr
Keep plugging and don't sell yourself short.

Answer 2

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