Mathematics
Two trains leave a railway station at same time. The first train travels due west and the second train due north. The first train travels 5 km/hr faster than the second train. If after 2 hours, they are 50 km apart, find the speed of each train.
Quadratic Equations
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Answer
Let speed of second train be x km/hr and first be (x + 5) km/hr.
According to figure,
Let O be the position where trains leave
Distance travelled by first train OA = 2(x + 5) km
Distance travelled by second train OB = 2x km
By pythagoras theorem we get,
⇒ AB2 = OA2 + OB2
⇒ 502 = [2(x + 5)]2 + (2x)2
⇒ 502 = 4(x + 5)2 + 4x2
⇒ 2500 = 4(x2 + 25 + 10x) + 4x2
⇒ 2500 = 4x2 + 100 + 40x + 4x2
⇒ 8x2 + 40x - 2400 = 0
⇒ 8(x2 + 5x - 300) = 0
⇒ x2 + 5x - 300 = 0
⇒ x2 + 20x - 15x - 300 = 0
⇒ x(x + 20) - 15(x + 20) = 0
⇒ (x - 15)(x + 20) = 0
⇒ x - 15 = 0 or x + 20 = 0
⇒ x = 15 or x = -20.
Since, speed cannot be negative,
∴ x ≠ -20.
∴ x = 15 and x + 5 = 20
Hence, speed of first train = 20 km/hr and second train = 15 km/hr.
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Case study:
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Malik travels by a Jeep and Rakesh by a car.
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