SOLUTION: A woman drives 10 miles then increases her speed by 10 miles per hour and drives another 25 miles. Find the original speed if she drove for 45 minutes

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A woman drives 10 miles then increases her speed by 10 miles per hour and drives another 25 miles. Find the original speed if she drove for 45 minutes      Log On


   

Question 1009462: A woman drives 10 miles then increases her speed by 10 miles per hour and drives another 25 miles. Find the original speed if she drove for 45 minutes
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Let the original speed be s%28+mil%2Fh%29.
distance:
d=st=>10mil=st
time: t=10%2Fs
d=%28s%2B10%29t=>25mil=st
time: t=25%2F%28s%2B10%29
if time t=45min=>t=%2845%2F60%29h=>t=0.75h
then we have:
10%2Fs+%2B+25%2F%28s%2B10%29+=+0.75

10%28s%2B10%29+%2Fs%28s%2B10%29++%2B+25%2F%28s%2B10%29+=+0.75

%28%2810s%2B100%29++%2B+25s%29%2Fs%28s%2B10%29+=+0.75

%2810s%2B100+%2B+25s%29=+0.75%2As%28s%2B10%29+

100+%2B+35s=+0.75%28s%5E2%2B10s%29+

100+%2B+35s=+0.75s%5E2%2B7.5s+

0=+0.75s%5E2%2B7.5s-35s-100

+0.75s%5E2-27.5s-100=0..........use quadratic formula

s+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+



s+=+%2827.5+%2B-+sqrt%28756.25%2B300+%29%29%2F1.5+

s+=+%2827.5+%2B-+sqrt%281056.25+%29%29%2F1.5+

s+=+%2827.5+%2B-+32.5%29%2F1.5+

we need only positive solution, speed cannot be negative value

s+=+%2827.5+%2B+32.5%29%2F1.5+

s+=+60%2F1.5+

highlight%28s+=+40mph%29-> original speed