After making a trip of 126 km, Victor found that if he had increased his average speed by 8 km/hr he could have saved 1 hour on the trip. Find his original speed using variables.

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After making a trip of 126 km, Victor found that if he had increased his average speed by 8 km/hr he could have saved 1 hour on the trip. Find his original speed using variables.

Mathematics
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Start out using the d=rt formula d is distance, r rate in km per hr, t is time in hours. 126/r = t is one equation Eq1 126/(r+8)= t-1 is the other equation Eq2 There you have it two equations two unknowns, something that can be solved Let us work on Eq2 so that it is a function of t: (126/(r+x)) + 1 = t this is still Eq2 but using algebra t is isolated. Since both equations now equal t we can write and then solve. (126/(r+8)) + 1 = 126/r You can solve it now using the quadratic formula.
The equation becomes \[r ^{2}+84r-1008=0\]

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