SOLUTION: In a 30 mile race between Joe and Frank, Joe started an hour after frank and finished an hour before Frank. Joe's average speed was 1 mile per hour faster than Franks. Find Joe and

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Question 675983: In a 30 mile race between Joe and Frank, Joe started an hour after frank and finished an hour before Frank. Joe's average speed was 1 mile per hour faster than Franks. Find Joe and Frank's average seed during the race.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = Frank's speed in mi/hr
+s+%2B+1+ = Joe's speed in mi/hr
+s%2A1+=+s+ = Frank's head start in miles
+t+ = Frank's time after his head start
+t+-+1+ = Joe's time after Frank's head start
---------------
Frank's equation:
(1) +30+-+s++=+s%2At+
Joe's equation:
(2) +30+=+%28+s+%2B+1+%29%2A%28+t+-+1+%29+
--------------------------
(2) +30+=+s%2At+%2B+t+-+s+-+1+
(2) +30+=+t%2A%28+s+%2B+1+%29+-+%28+s+%2B+1+%29+
and
(1) +t+=+%28+30+-+s+%29+%2F+s+
Substitute this into (2)
(2) +30+=+%281%2Fs%29%2A%28+30+-+s+%29%2A%28+s+%2B+1+%29+-+%28+s+%2B+1+%29+
(2) +30+=+%281%2Fs%29%2A%28+30s+-+s%5E2+%2B+30+-+s+%29+-+%28+s+%2B+1+%29+
(2) +30+=+30+-+s+%2B+30%2Fs+-+1+-+s+-+1+
(2) +30%2Fs+=+2s+%2B+2+
(2) +30+=+2s%5E2+%2B+2s+
(2) +s%5E2+%2B+s+-+15+=+0+
Use quadratic formula
+s+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+1+
+c+=+-15+
+s+=+%28-1+%2B-+sqrt%28+1%5E2+-+4%2A1%2A%28-15%29+%29%29+%2F+%282%2A1%29+
+s+=+%28-1+%2B-+sqrt%28+1+%2B+60+%29%29+%2F+2+
+s+=+%28-1+%2B+sqrt%28+61+%29%29+%2F+2+
+s+=+%28+-1+%2B+7.8103+%29+%2F+2+
+s+=+6.8103%2F2+
+s+=+3.4051+ mi/hr = Frank's speed
+s+%2B+1+=+4.4051+ mi/hr = Joe's speed
My math could have got messed up- check it