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Two roads intersect perpendicularly. Alex walks toward the north from a point that is 1200 meters South of the intersection point. Bob walks from the intersection point toward east. They start at the same time. After ten minutes both of them are the same distance away from the intersection. After 100 minutes both of them are the same distance from the intersection again. How far away is Alex from the intersection now?

Jun 11, 2019

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Let the distance that Bob walks east in 10 minutes  =  x

So.....he is x meters from the intersection in 10 minutes

And Alex is  x meters from the intersection after 10 minutes

So....the distance that Alex walks in 10 minutes must be (1200 - x)

So.....in 100 minutes, Bob must be 10x meters east of the intersection

And  Alex must be the same distance north of the intersection

So....in 100 minutes Alex  walks  10(1200-x) meters......and this distance must equal the 1200 meters to the intersection plus the 10x meters north of the intersection

So

10 (1200 - x) = 10x + 1200   simplify

12000 - 10x = 10x + 1200

10800 = 20x     divide by 20

540 = x

So...the distance that Alex is from the intersection after 100 minutes is

Total distance walked - 1200 m

10 (1200 - x) - 1200 =

10(1200 -540) - 1200 =  10(660) - 1200 = 6600 - 1200 =    5400 m

Note that Bob  is the same distance from the intersection = 10x =  10(540) = 5400 m

Jun 11, 2019
edited by CPhill  Jun 11, 2019