DIRECTIONS for the following three questions

These questions are based on the situation given below:

A road network (shown in the figure below) connects cities A, B, C and D. All road segments are straight lines. D is the midpoint on the road connecting A and C. Roads AB and BC are at right angles to each other with BC shorter than AB. The segment AB is 100 km long. Ms. X and Mr. Y leave A at 8:00 am, take different routes to city C and reach at the same time. X takes the highway from A to B to C and travels at an average speed of 61.875 km per hour. Y takes the direct route AC and travels at 45 km per hour on segment AD. Y's speed on segment DC is 55 km per hour.




Question 50

What is the length of the road segment BD?


$$BC^2$$ + 10000 = $$AC^2$$.

$$\frac{BC+100}{61.875}$$ = $$\frac{AC}{49.5}$$ => $$\frac{BC+100}{AC}$$ = 1.25 = > BC = 1.25AC - 100

On solving these equations, we get AC as 105 and BC a 31.

Let the point B be (0,0) => A = (0, -100) and C = (31,0)

D = Mid point of AC = (15.5, -50)

BD = $$\sqrt{15.5^2+50^2}$$ = 52.5 (approximately).

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