SOLUTION: Kari took her new motorcycle for a drive to a town 300 miles away and then back home. Consider her speed to be constant in both directions of travel. On her return trip, she trave

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Kari took her new motorcycle for a drive to a town 300 miles away and then back home. Consider her speed to be constant in both directions of travel. On her return trip, she trave      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 684009: Kari took her new motorcycle for a drive to a town 300 miles away and then back home. Consider her speed to be constant in both directions of travel. On her return trip, she traveled 10 mph faster and made the return trip in 1 hour less time. Find her speed and time in each direction. Show a clear and logical approach to the problem
I'm having trouble figuring out the equation.. Thanks for your help.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = her speed in mi/hr going to town
Let +t+ = her time in hrs going to town
+s+%2B+10+ = her speed in mi/hr going back home
+t+-+1+ = her time in hrs going back home
----------------
given:
Going to town:
(1) +300+=+s%2At+
Going back home:
(2) +300+=+%28+s+%2B+10+%29%2A%28+t+-+1+%29+
----------------------------
(1) +t+=+300%2Fs+
and
(2) +300+=+s%2At+%2B+10t+-+s+-+10+
Substitute (1) into (2)
(2) +300+=+s%2A%28300%2Fs%29+%2B+10%2A%28+300%2Fs%29+-+s+-+10+
(2) +300+=+300+%2B+3000%2Fs+-+s+-+10+
(2) +3000%2Fs+-+s+=+10+
Multiply both sides by +s+
(2) +3000+-+s%5E2+=+10s+
(2) +s%5E2+%2B+10s+-+3000+=+0+
Use quadratic formula
+s+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+10+
+c+=+-3000+
+s+=+%28-10+%2B-+sqrt%28+10%5E2+-+4%2A1%2A%28-3000%29+%29%29+%2F+%282%2A1%29+
+s+=+%28-10+%2B-+sqrt%28+100+%2B+12000+%29%29+%2F+2+
+s+=+%28-10+%2B-+sqrt%28+12100+%29%29+%2F+2+
+s+=+%28+-10+%2B+110+%29+%2F+2+
+s+=+100+%2F+2+
+s+=+50+
and, since
(1) +t+=+300%2Fs+
(1) +t+=+300+%2F+50+
(1) +t+=+6+
and
+s+%2B+10+=+60+
+t+-+1+=+5+
--------------------
Her speed going to town is 50 mi/hr
Her time going to town is 6 hrs
Her speed going back home is 60 mi/hr
Her time going back home is 5 hrs
---------------------
check:
(2) +300+=+%28+s+%2B+10+%29%2A%28+t+-+1+%29+
(2) +300+=+60%2A5+
(2) +300+=+300+
and
(1) +300+=+s%2At+
(1) +300+=+50%2A6+
(1) +300+=+300+
OK