Steve S. answered • 02/21/14

Tutoring in Precalculus, Trig, and Differential Calculus

After reading Robert's answer, I would guess that the correct equation is:

t(v) = 253/(v+70) + 413/(v+75)

Then you drove 253 miles where the speed limit was 70 mph and 413 miles where the speed limit was 75.

Then t(2) = 253/72 + 413/77 = 253/72 + 59/11.

t(2) = (216 + 37)/72 + (55 + 4)/11

t(2) = 3 + 37/72 + 5 + 4/11

t(2) = 8 + 37/72 + 4/11

t(2) ≈ 8 + 0.5 + 0.4 ≈ 8.9 hours

How close is our estimate?

t(2) = 8 + 37/72 + 4/11

t(2) ≈ 8 + 0.51388888888889 + 0.36363636363636 ≈ 8.87752525252525 hours

Darn close!

And the estimate did not use a calculator (in case you forgot it, it's broken, the batteries are dead, you lent it to a friend, the dog chewed it up, it's a new whiz-bang graphing calculator your parent's bought you for your birthday and you don't know how to use it because you didn't read the user's manual and do the practice problems, etc.)