A car made a run of 390 km in x hours. If the speed had been 4 km/ hrs more, it would have taken 2 hours less for the journey. Find the value of x.
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(1) Distance = 390 km
Time = x hours
Speed = Distance/Time
v = 390/x
(2) If speed had been 4km/hr more ;
Distance = 390
Time = x-2
v' = (390/x)+4
= (390+4x)/x
390/(x-2) = (390+4x)/x
390x = 390x+4x^2-780-8x
4x^2-8x-780 = 0
2x^2 - 4x - 390 = 0
2x^2 +26x-30x-390 = 0
2x(x+13) -30(x+13) = 0
(2x-30) (x+13) = 0
x = 30 & -13
As the time cannot be negative, hence the value of x is 30 hr
Time = x hours
Speed = Distance/Time
v = 390/x
(2) If speed had been 4km/hr more ;
Distance = 390
Time = x-2
v' = (390/x)+4
= (390+4x)/x
390/(x-2) = (390+4x)/x
390x = 390x+4x^2-780-8x
4x^2-8x-780 = 0
2x^2 - 4x - 390 = 0
2x^2 +26x-30x-390 = 0
2x(x+13) -30(x+13) = 0
(2x-30) (x+13) = 0
x = 30 & -13
As the time cannot be negative, hence the value of x is 30 hr
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1
this is ur answer time is 15 hrs
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