We need to find: traveled miles k hours and 10 units of fuel.
From the linear equation: Answer = \(k*(3*10+4)\) = 34k
Data:
x miles in k hours at 7 units/hr: equation: \(x =k*(3*7+4)\) = 25k
=> x=25k or k = x/25 (equation 1)
40% extra miles = 1.4 x
one hour less = k-1 hours
5 units/hr extra fuel = 7+5 = 12
Equation \(1.4x=(k-1)*(3*12+4)\)
\(=> 14x = (k-1)*(40)*10\)
\(=> 14x= 400k-400\)
\(=> 14x = 16x - 400\) (substitute k= x/25)
\(=> 2x = 400\)
\(=> x = 200\)
\(=> k = 200/25 = 8\) (substitute back from equation 1: k=x/25)
Required Answer = 34k = 34*8 = 272
While solving the equation, you can either substitute x or k, depending on the numbers in hand and involved calculation.
I substituted k = x/25, because my numbers were becoming large and 400 was easily divisible by 25.
It was quicker to solve x first than k.
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