two trains leave a railway station at the same time. the first train travels due west and the second train due north.the first travels 5km/hr faster than the second train.if after two hours,they are 50km apart ,find the average speedof each train
Answers
Answer:
SolutionLet the speed of the second train = x km/hr
The speed of the first train = x+5 km/hr
Distance covered after two hours by the first train is 2(x+5) km.
Distance covered by the second train after two hours is 2x km.
(2x)^2 + 4(x+5)^2=(50)^2 (Using pythagoras theorem)
Solve
We get x=-20 and x=15
The speed of the first train = 15+5=20km/hr
Explanation:
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Speed of first train is 20 Km/h and speed of 2nd train is 15 Km/h
➣ Let the 2nd train travel at X km/h
➣Then, the speed of a train is (5 +x) Km/hour.
➣ let the two trains live from station M.
➣ Distance travelled by first train in 2 hours
= MA = 2(x+5) Km.
➣ Distance travelled by second train in 2 hours
= MB = 2x Km
AB²= MB²+MA²
⟹ 50²=(2(x+5)²+(2x)²
⟹ 2500 = (2x+10)² + 4x²
⟹8x² + 40x - 2400 = 0
⟹x² + 5x - 300 = 0
⟹x² + 20x -15x - 300 = 0
⟹x(x + 20) - 15(x + 20) = 0
⟹ (x + 20)(x -15) = 0
Taking x = 15 , the speed of second train is 15 Km/h and speed of first train is 20 Km/h