SOLUTION: On a 370-mile trip, Andy averaged 5 miles per hour faster for the last 160 miles than he did for the first 210 miles. The entire trip took 10 hours. How fast did he travel for the

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Question 678035: On a 370-mile trip, Andy averaged 5 miles per hour faster for the last 160 miles than he did for the first 210 miles. The entire trip took 10 hours. How fast did he travel for the first 210 miles?
I have tried so many different ways to solve and just can't! my teacher didn't go over any of this!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You need 2 equations, 1 for the first 210 miles
and another for the last 160 miles
Let +t+ = his time in hrs for the 1st 210 miles
Let +s+ = his speed for the 1st 210 miles
+10+-+t+ = his time in hrs for the last 160 miles
+s+%2B+5+ = his speed for the last 160 miles
--------------------------------------
Equation for the first 210 miles:
(1) +210+=+s%2At+
Equation for the last 160 miles
(2) +160+=+%28+s+%2B+5+%29%2A%28+10+-+t+%29+
----------------------------
(2) +160+=+10s+%2B+50+-+s%2At+-+5t+
(2) +10s+-+s%2At+-+5t+=+110+
and
(1) +s+=+210%2Ft+
Substitute (1) into (2)
(2) +10%2A%28210%2Ft%29+-+%28210%2Ft%29%2At+-+5t+=+110+
(2) +2100%2Ft+-+210+-+5t+=+110+
Multiply both sides by +t+
(2) +2100+-+210t+-+5t%5E2+=+110t+
(2) +5t%5E2+%2B+320t+=+2100+
(2) +t%5E2+%2B+64t+=+420+
complete the square
(2) +t%5E2+%2B+64t+%2B+%2864%2F2%29%5E2+=+420+%2B+%2864%2F2%29%5E2+
(2) +t%5E2+%2B+64t+%2B+1024+=+420+%2B+1024+
(2) +%28+t+%2B+32+%29%5E2+=+1444+
Take the square root of both sides
(2) +t+%2B+32+=+38+
(2) +t+=+6+
and, since
(1) +210+=+s%2At+
(1) +210+=+s%2A6+
(1) +s+=+210%2F6+
(1) +s+=+35+
His speed for the 1st 210 miles was 35 mi/hr
check:
(2) +160+=+%28+s+%2B+5+%29%2A%28+10+-+t+%29+
(2) +160+=+%28+35+%2B+5+%29%2A%28+10+-+t+%29+
(2) +160+=+40%2A%28+10+-+t+%29+
(2) +10+-+t+=+4+
(2) +t+=+6+
OK