Question

Study the figure below and answer the question:

(Figure shows points A, B, C, D with routes ABCD, ABD, ACD, ACBD)

Four persons walk from Point A to Point D following different routes. The one following ABCD takes 70 minutes. Another person takes 45 minutes following ABD. The third person takes 30 minutes following route ACD. The last person takes 65 minutes following route ACBD. If all were to walk at the same speed, how long will it take to go from point B to point C?

Accepted Answer

C. Let time for segment $XY$ be $t(XY)$. 1) $t(AB) + t(BC) + t(CD) = 70$ 2) $t(AB) + t(BD) = 45$ 3) $t(AC) + t(CD) = 30$ 4) $t(AC) + t(BC) + t(BD) = 65$ Add (1) and (4): $$t(AB) + t(AC) + 2 t(BC) + t(CD) + t(BD) = 135$$ Substitute (2) and (3): $$45 + 30 + 2 t(BC) = 135 \implies 2 t(BC) = 60 \implies t(BC) = 30 	ext{ min.}$$

Speed, Distance and Time: Route Timings

Explanation

Practise this under exam conditions