SOLUTION: Miguel walked 10 km into the country. He returned walking 3 km/h slower. The total time for the round trip was 7 h. How fast did he walk on each part of the trip?

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Question 1026000: Miguel walked 10 km into the country. He returned walking 3 km/h slower. The total time for the round trip was 7 h. How fast did he walk on each part of the trip?
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Miguel walked 10 km into the country. He returned walking 3 km/h slower. The total time for the round trip was 7 h. How fast did he walk on each part of the trip?
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r = rate going
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10/r + 10/(r-3) = 7
Solve for r

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = his speed walking into country in km/hr
Let +t+ = his time walking into country in hrs
+s+-+3+ = his speed returning in km/hr
+7+-+t+ = his time returning in hrs
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His equation for walking into country:
(1) +10+=+s%2At+
His equation for returning from country
(2) +10+=+%28+s+-+3+%29%2A%28+7+-+t+%29+
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(1) +t+=+10%2Fs+
(2) +10+=+7s+-+21+-+s%2At+%2B+3t+
(2) +t%2A%28+3+-+s+%29+%2B+7s+=+31+
Substitute (1) into (2)
(2) %2810%2Fs%29%2A%28+3+-+s+%29+%2B+7s+=+31+
(2) +10%2A%28+3+-+s+%29+%2B+7s%5E2+=+31s+
(2) +30+-+10s+%2B+7s%5E2+-+31s+=+0+
(2) +7s%5E2+-+41s+%2B+30+=+0+
use the quadratic formula
+s+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+7+
+b+=+-41+
+c+=+30+
+s+=+%28+-%28-41%29+%2B-+sqrt%28%28-41%29%5E2+-+4%2A7%2A30+%29%29+%2F+%282%2A7%29+
+s+=+%28+41+%2B-+sqrt%28+1681+-+840+%29%29+%2F+14+
+s+=+%28+41+%2B-+sqrt%28+841%29%29+%2F+14+
+s+=+%28+41+%2B+29%29+%2F+14+
+s+=+70%2F14+
+s+=+5+
and
+s+=+%28+41+-+29%29+%2F+14+
+s+=+12%2F14+
+s+=+6%2F7+
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I can't subtract +3+ from +6%2F7+,
so +s+=+5+ must be the answer
+s+-+3+=+2+
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his speed walking into country was 5 km/hr
his speed returning was 2 km/hr
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check:
(1) +10+=+s%2At+
(1) +10+=+5%2At+
(1) +t+=+2+
and
(2) +10+=+%28+5+-+3+%29%2A%28+7+-+t+%29+
(2) +10+=+2%2A%28+7+-+t+%29+
(2) +10+=+14+-+2t+
(2) +2t+=+4+
(2) +t+=+2+
OK