<PRE><B>Question 825324</B>
a man travels 200kms with a uniform speed of xkm per hour, the distance could have been covered in 2hours less had the speed been (x+5)km per hour.
Calculate the value of x.
:
Write time equation; time = dist/speed
:
{{{200/x}}} - {{{200/((x+5))}}} = 2
multip0ly by x(x+5), cancel the denominators
200(x+5) - 200x = 2x(x+5)
200x + 1000 - 200x = 2x^2 + 10x
Combine on the right to form a quadratic equation
0 = 2x^2 + 10x - 1000 
simplify, divide by 2
x^2 + 5x - 500 = 0
factors to
(x+25)(x-20) = 0
positive solution
x = 20
:
:
Check this by finding the times
200/20 = 10 hrs
200/25 = 8 hrs
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