Question

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.

Answer 1

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.

Answer 2

The equation becomes
\[r ^{2}+84r-1008=0\]