Ashish goes to his friends house which is 12km away from his house. He covers half of the
distance at a speed of x km per hour and the remaining at x+2 km per hour. If he takes
2 hrs 30 min to cover the whole distance, find the value of x.
Answers
Answer: Hello Friend Here Is Your Answer
Distance Is 4 km/hr
Step-by-step explanation:
• Distance (s) = 12 km
• Time (t) = 2 hours 30 minutes
=> 2.5 hrs. =
• Speed during 1st half = x km/hr.
• Speed during 2nd half = (x + 2) km/hr.
_____________ [ GIVEN ]
• We have to find the value of x. (distance)
_______________________________
Now..
» Speed =
Time =
a) Time taken for first half =
=> Time = ________ (eq 1)
b) Time taken for second half =
=> Time = ________ ( eq 2)
» Add (eq 1) & (eq 2)
=> + =
=> =
=> =
Cross-multiply them
=> 2(12x + 12) = 5(x² + 2x)
=> 24x + 24 = 5x² + 10x
=> 5x² + 10x - 24x - 24 = 0
=> 5x² - 14x - 24 = 0
=> 5x² - 20x + 6x - 24 = 0
=> 5x(x - 4) +6(x - 4) = 0
=> (5x + 6) (x - 4) = 0
=> x = -6/5 (neglected because time can't be negative)
So..
=> x = 4
_____________________________
Distance = 4 km/hr.
_________ [ ANSWER ]
______________________________
Thank You!
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Step-by-step explanation:
Distance (s) = 12 km
• Time (t) = 2 hours 30 minutes
=> 2.5 hrs. = \dfrac{5}{2}
2
5
• Speed during 1st half = x km/hr.
• Speed during 2nd half = (x + 2) km/hr.
_____________ [ GIVEN ]
• We have to find the value of x. (distance)
_______________________________
Now..
» Speed = \dfrac{Distance}{Time}
Time
Distance
Time = \dfrac{Distance}{Speed}
Speed
Distance
a) Time taken for first half = \dfrac{Distance}{Speed}
Speed
Distance
=> Time = \dfrac{6}{x}
x
6
________ (eq 1)
b) Time taken for second half = \dfrac{Distance}{Speed}
Speed
Distance
=> Time = \dfrac{6}{x+2}
x+2
6
________ ( eq 2)
» Add (eq 1) & (eq 2)
=> \dfrac{6}{x}
x
6
+ \dfrac{6}{x+2}
x+2
6
= \dfrac{5}{2}
2
5
=> \dfrac{ 6x\: + \:12 \: + \: 6x }{ {x}^{2} \: + \: 2x }
x
2
+2x
6x+12+6x
= \dfrac{5}{2}
2
5
=> \dfrac{12 x\: + \: 12 }{ {x}^{2} \: + \: 2x }
x
2
+2x
12x+12
= \dfrac{5}{2}
2
5
Cross-multiply them
=> 2(12x + 12) = 5(x² + 2x)
=> 24x + 24 = 5x² + 10x
=> 5x² + 10x - 24x - 24 = 0
=> 5x² - 14x - 24 = 0
=> 5x² - 20x + 6x - 24 = 0
=> 5x(x - 4) +6(x - 4) = 0
=> (5x + 6) (x - 4) = 0
=> x = -6/5 (neglected because time can't be negative)
So..
=> x = 4
_____________________________
Distance = 4 km/hr.
_________ [ ANSWER ]
______________________________