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 68 miles with the wind, he could go only 30 miles against the wind. What is his normal bicycling speed with no wind?

Answer 1

d = r · t ⇒ t = d/r

going

t = 54/(r + 4)

coming

t = 30/(r - 4)

54/(r + 4) = 30/(r - 4) times are equal

54(r - 4) = 30(r + 4) product means/extremes

54r - 216 = 30r + 120 distribute

24r - 216 = 120 subtract 30r from both sides

24r = 336 add 216 to both sides

r = 14 divide both sides by 24

Alfonso bikes at 24 mph.