SOLUTION: David and Keith are route drivers for a fast -photo company. David route is 80 miles, and Keith’s is 100 miles. Keith averages 10 mph more than David and finishes his route 10 minu

Algebra ->  Equations -> SOLUTION: David and Keith are route drivers for a fast -photo company. David route is 80 miles, and Keith’s is 100 miles. Keith averages 10 mph more than David and finishes his route 10 minu      Log On


   

Question 323778: David and Keith are route drivers for a fast -photo company. David route is 80 miles, and Keith’s is 100 miles. Keith averages 10 mph more than David and finishes his route 10 minutes before David. What is David’s speed.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Equation for David:
d+=+r%2At
80+=+r%2At
Equation for Keith:
100+=+%28r+%2B+10%29%2A%28t+-+1%2F6%29
100+=+rt+%2B+10t+-+%281%2F6%29%2Ar+-+10%2F6
By substitution:
100+=+80+%2B+10t+-+%281%2F6%29%2A%2880%2Ft%29+-+10%2F6
20+=+10t+-+%2840%2F%283t%29+-+5%2F3%29
Multiply both sides by 3t
60t+=+30t%5E2+-+40+-+5t
30t%5E2+-+65t+-+40+=+0
6t%5E2+-+13t+-+8+=+0
Use the quadratic formula
t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+6
b+=+-13
c+=+-8
t+=+%28-%28-13%29+%2B-+sqrt%28+%28-13%29%5E2-4%2A6%2A%28-8%29+%29%29%2F%282%2A6%29+
t+=+%28+13+%2B-+sqrt%28++169+%2B+192+%29%29%2F12+
t+=+%28+13+%2B-+sqrt%28++361+%29%29%2F12+
t+=+%28+13+%2B-+19%29%2F12+
t+=+32%2F12
t+=+8%2F3
For David:
80+=+r%2At
r+=+80%2F%288%2F3%29
r+=+240%2F8
r+=+30
David's speed is 30 mi/hr
check:
For Keith
100+=+%28r+%2B+10%29%2A%28t+-+1%2F6%29
100+=+%2830+%2B+10%29%2A%288%2F3+-+1%2F6%29
100+=+40%2A%2816%2F6+-+1%2F6%29
100+=+40%2A%2815%2F6%29
600+=+40%2A15
600+=+600
OK