A bus covers 300 km at a uniform speed. Due to an emergency, its speed increased by 10km/hr and so the bus reaches the destination two and a half hours earlier. Assuming the initial uniform speed to be x km/hr, which among the following quadratic equations is correct.
Answers
Step-by-step explanation:
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Given :- A bus covers 300 km at a uniform speed. Due to an emergency, its speed increased by 10km/hr and so the bus reaches the destination two and a half hours earlier.
To Find :- The quadratic equation to find initial uniform speed .
Solution :-
Let us assume that, initial uniform speed is x km/h .
So,
→ Time taken to cover 300 km = Distance / speed = (300/x) hours .
now,
→ New speed = (x + 10) km/h
then,
→ New time taken to cover 300 km = Distance / speed = 300/(x + 10) hours .
then,
→ Time saved = 2 and a half hour = 2(1/2) = (5/2) hours .
→ (300/x) - {300(x + 10)} = (5/2)
→ [300(x + 10) - 300x]/x(x + 10) = (5/2)
→ 3000/(x² + 10x) = 5/2
→ x² + 10x = 1200
→ x² + 10x - 1200 = 0 { Required quadratic equation .}
solving this we get,
→ x² + 40x - 30x - 1200 = 0
→ x(x + 40) - 30(x + 40) = 0
→ (x + 40)(x - 30) = 0
→ x = 30 or (-40)
since speed cant be in negative , (-40) is not possible .
Therefore, the initial uniform speed of bus is 30 km/h .
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