SOLUTION: A man cycled a distance of 42km from his village. On his return journey he increased his speed by 2km/hr and took half an hour less. Calculate the average speed on the journey from

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Question 824121: A man cycled a distance of 42km from his village. On his return journey he increased his speed by 2km/hr and took half an hour less. Calculate the average speed on the journey from his village.
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A man cycled a distance of 42km from his village. On his return journey he increased his speed by 2km/hr and took half an hour less. Calculate the average speed on the journey from his village.
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d = r*t
42 = r*t
t = 42/r
t - 0.5 = 42/(r+2)
42/r = 0.5 + 42/(r+2)
Solve for r

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +r+ = his rate going from the village in km/hr
Let +t+ = his time in hrs going from the village
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Equation going from the village:
(1) +42+=+r%2At+
Equation for return journey:
(2) +42+=+%28+r%2B2+%29%2A%28+t+-+.5+%29+
-------------------------
(2) +42+=+r%2At+%2B+2t+-+.5r+-+1+
(2) +43+%2B+.5r+=+r%2At+%2B+2t+
(2) +43+%2B+.5r+=+%28+r+%2B+2+%29%2At+
(2) +t+=+%28+43+%2B+.5r+%29+%2F+%28+r+%2B+2+%29+
-----------------------------
(1) +42%2Fr+=+t+
By substitution:
(1) +42%2Fr+=+%28+43+%2B+.5r+%29+%2F+%28+r+%2B+2+%29+
Multiply both sides by +r%2A%28+r+%2B+2+%29+
(1) +42%2A%28+r%2B2+%29+=+%28+43+%2B+.5r+%29%2Ar+
(1) +42r+%2B+84+=+43r+%2B+.5r%5E2+
(1) +.5r%5E2+%2B+r+-+84+=+0+
(1) +r%5E2+%2B+2r+-+168+=+0+
-----------------------
+r+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+2+
+c+=+-42+
+r+=+%28-2+%2B-+sqrt%28+2%5E2+-+4%2A1%2A%28-168%29+%29%29+%2F+%282%2A1%29+
+r+=+%28-2+%2B-+sqrt%28+4+%2B+672+%29%29+%2F+2+
+r+=+%28-2+%2B-+sqrt%28+676+%29%29+%2F+2+
+r+=+%28-2+%2B+26%29+%2F+2+
+r+=++-1+%2B+13%0D%0A%7B%7B%7B+r+=+12+
His average rate traveling from the village was 12 km/hr
check:
(1) +42+=+r%2At+
(1) +t+=+42%2F12+
(1) +t+=+3.5+
-----------------
(2) +42+=+%28+r%2B2+%29%2A%28+t+-+.5+%29+
(2) +42+=+%28+12+%2B+2+%29%2A%28+3.5+-+.5+%29+
(2) +42+=+14%2A3+
(2) +42+=+42+
OK