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Question
Two trains leave a railway station at the same time. The first train travels due west and the second train due north. The first train travels at a speed of `(20 "km")/"hr"` and the second train travels at `(30 "km")/"hr"`. After 2 hours, what is the distance between them?
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Solution
A is the position of the 1st train.
B is the position of the 2nd train.
Distance Covered in 2 hours
OA = 2 × 20 = 40 km
OB = 2 × 30 = 60 km
Distance between the train after 2 hours
AB = `sqrt("OA"^2 + "OB"^2)`
= `sqrt(40^2 + 60^2)`
= `sqrt(1600 + 3600)`
= `sqrt(5200)` or `sqrt(52 xx 100)`
= `10sqrt(4 xx 13)`
= `20sqrt(13)`
= 72.11 km
Distance between the two train = 72.11 km or `20sqrt(13) "km"`
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