SOLUTION: In a certain number of hours a woman travelled 2km . If she had travelled 7km more per hour, it would have taken her 3hr less to make the journey. How many kilometres did she tra

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Question 735018: In a certain number of hours a woman travelled 2km . If she had travelled 7km more per hour, it would have taken her 3hr less to make the journey. How many kilometres did she travel per hour?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Actual trip:
+d+=+r%2At+
(1) +2+=+r%2At+
-----------
"what if " trip:
(2) +2+=+%28+r+%2B+7+%29%2A%28+t+-+3+%29+
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There are 2 equations and 2 unknowns,
so it's solvable
(2) +2+=+r%2At+%2B+7t+-+3r+-+21+
and
(1) +t+=+2%2Fr+
By substitution:
(2) +2+=+r%2A%282%2Fr%29+%2B+7%2A%282%2Fr%29+-+3r+-+21+
(2) +2+=+2+%2B+14%2Fr+-+3r+-+21+
(2) +3r+%2B+21+=+14%2Fr+
Multiply both sides by +r+
(2) +3r%5E2+%2B+21r+=+14+
(2) +3r%5E2+%2B+21r+-+14+=+0+
Use quadratic formula
+r+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+3+
+b+=+21+
+c+=+-14+
+r+=+%28+-21+%2B-+sqrt%28+21%5E2+-+4%2A3%2A%28-14%29+%29%29+%2F+%282%2A3%29+
+r+=+%28+-21+%2B-+sqrt%28+441+%2B+168+%29%29+%2F+6+
+r+=+%28+-21+%2B-+sqrt%28+609+%29%29+%2F+6+
+r+=+%28+-21+%2B+24.68+%29+%2F+6+
+r+=+3.68%2F6+
+r+=+.6133+
She traveled .6133 km/hr
check:
(1) +2+=+r%2At+
+t+=+2%2F.6133+
+t+=+3.26+ hrs
and
(2) +2+=+%28+r+%2B+7+%29%2A%28+t+-+3+%29+
(2) +2+=+%28+.6133+%2B+7+%29%2A%28+3.26+-+3+%29+
(2) +2+=+7.6133%2A.26+
(2) +2+=+1.979+
I think the error is due to rounding off