Question

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?

Answer 1

34-4x=18+4x
16=8x
x=2
18+4*2=26
26/2 =
13mph

Answer 2

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