SOLUTION: During rush hour, Fernando can drive 40 miles using the side roads in the same time that it takes to travel 30 miles on the freeway. If Fernando's rate on the side roads is 7 mi/h

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: During rush hour, Fernando can drive 40 miles using the side roads in the same time that it takes to travel 30 miles on the freeway. If Fernando's rate on the side roads is 7 mi/h      Log On


   

Question 89099: During rush hour, Fernando can drive 40 miles using the side roads in the same time that it takes to travel 30 miles on the freeway. If Fernando's rate on the side roads is 7 mi/h faster than his rate on the freeway, find his rate on the side roads.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
s = rate on sides roads
f = rate on freeway
s+=+40%2Ft is his rate on side roads. We don't actually know what t is, but
f+=+30%2Ft is his rate on the freeways and it's the same t, so the ratio
%2840%2Ft%29+%2F+%2830%2Ft%29+=+4%2F3 is the ratio os his rate on side roads to
his rate on freeways
s%2Ff+=+4%2F3
multiply both siides by f
s+=+%284%2F3%29%2Af
Also given is s+=+f+%2B+7
%284%2F3%29%2Af+=+f+%2B+7
4f+=+3f+%2B+21
f+=+21
s+=+f+%2B+7
s+=+28
Is the ratio true? s%2Ff+=+4%2F3
28%2F21+=+4%2F3 Yes
So, his rate on the side roads is 28 mph