Translate problem into an equation and solve.
thiago and brandon are driving away from each other in opposite directions. if brandon’s speed is 70 mph and thiago's speed is 80 mph, how many hours will it be before the two are 225 miles apart?

1.5 hours

Step-by-step explanation:

If Thiago and Brandon move in opposite directions at speeds of 80mph and 70mph then after 1 hour Thiago will have traveled 80 miles and Brandon will have traveled 70 miles.

Since they are in opposite directions then the distance is from

Then we know that after t hours have elapsed they are 225 miles

Then we pose the following equation

Now we solve for t

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

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step-by-step explanation:

told you