On a particular day, the wind added 4 miles per hour to Alfonso's rate when he was cycling with the wind and subtracted 4 miles per hour from his rate on his return trip. Alfonso found that in the same amount of time he could cycle 34 miles with the wind, he could go only 18 miles against the wind. What is his normal bicycling speed with no wind?

Question

Mathematics

Kayden Alexander

24 December, 01:26

On a particular day, the wind added 4 miles per hour to Alfonso's rate when he was cycling with the wind and subtracted 4 miles per hour from his rate on his return trip. Alfonso found that in the same amount of time he could cycle 34 miles with the wind, he could go only 18 miles against the wind. What is his normal bicycling speed with no wind?

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Answers (2)

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Arianna Glass · Answer 1

Ok so R=alfonso's rate

w=wind rate=4

d=rt

with wind rate is R+4

agaoins wind rate is R-4

with wind distance is 34

against is 18 miles

time is same

34 = (r+4) t

18 = (r-4) t

34 = (r+4) t

divide both sides by (r+4)

34 / (r+4) = t

18 = (r-4) t

divide both sides by (r-4)

18 / (r-4) = t

18 / (r-4) = t

34 / (r+4) = t

set equal to each other

18 / (r-4) = 34 / (r+4)

multiply both sides by (r-4) (r+4)

18 (r+4) = 34 (r-4)

distribute

18r+72=34r-136

subtract 18r from both sides

72=16r-136

add 136 to both sides

208=16r

divide both sides by 16

13mph

answer is 13mph with no wind

Ismael Colon · Answer 2

34-4x=18+4x

16=8x

x=2

18+4*2=26

26/2 =

13mph