SOLUTION: Marty drove his fully loaded moving van 270 miles to Memphis. With his van empty, Marty drove 15mi/h faster and made the return trip in 1.5 hours less. Find the speed going to Memp

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Marty drove his fully loaded moving van 270 miles to Memphis. With his van empty, Marty drove 15mi/h faster and made the return trip in 1.5 hours less. Find the speed going to Memp      Log On

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Question 442700: Marty drove his fully loaded moving van 270 miles to Memphis. With his van empty, Marty drove 15mi/h faster and made the return trip in 1.5 hours less. Find the speed going to Memphis
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Going to Memphis:
+d+=+r%2At+
Return trip:
+d+=+%28+r+%2B+15+%29%2A%28+t+-+1.5+%29+
-------------------
+r%2At+=+%28+r+%2B+15+%29%2A%28+t+-+1.5+%29+
+r%2At+=+r%2At+%2B+15t+-+1.5r+-+22.5+
+1.5r+=+15t+-+22.5+
+15r+=+150t+-+225+
+r+=+10t+-+15+
--------------------
given:
+d+=+270+
+t+=+d%2Fr+
+t+=+270%2Fr+
+r+=+10t+-+15+
+r+=+10%2A%28270%2Fr%29+-+15+
+r%5E2+=+2700+-+15r+
+r%5E2+%2B+15r+-+2700+=+0+
r+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+1+
+b+=+15+
+c+=+-2700+
r+=+%28-15+%2B-+sqrt%28+15%5E2+-+4%2A1%2A%28-2700%29+%29%29%2F%282%2A1%29+
r+=+%28-15+%2B-+sqrt%28+225+%2B+10800+%29%29+%2F+2+
r+=+%28-15+%2B-+sqrt%28+11025+%29%29+%2F+2+
r+=+%28-15+%2B+105%29+%2F+2+
r+=+90%2F2+
+r+=+45+
The speed going to Memphis was 45 mi/hr
check answer:
d+=+r%2At+
+270+=+45%2At+
+t+=+6+ hrs
and
+d+=+%28+r+%2B+15+%29%2A%28+t+-+1.5+%29+
+270+=+%28+45+%2B+15+%29%2A%28+6+-+1.5+%29+
+270+=+60%2A4.5+
+270+=+270+
OK