SOLUTION: 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 f

Algebra ->  Sequences-and-series -> SOLUTION: 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 f      Log On


   

Question 1142022: 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 57 miles with the wind, he could go only 33 miles against the wind.
What is his normal bicycling speed with no wind?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


If b is his speed without wind, then b+4 is his speed with the wind, and b-4 is his speed against the wind.

The time to bike 57 miles with the wind is 57/(b+4); the time to bike 33 miles against the wind is 33/(b-4).

The problem tells us those two times are the same, so

57%2F%28b%2B4%29+=+33%2F%28b-4%29

Solve using basic algebra....

Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
The time equation for this kinematic problem is this


    55%2F%28x%2B4%29 = 33%2F%28x-4%29.


where x is the speed at no wind, in miles per hour.


To solve the equation, cross-multiply


    57*(x-4) = 33*(x+4),


simplify and get


    57x - 33x = 33*4 + 57*4

    x = %2833%2A4+%2B+57%2A4%29%2F%2857-33%29 = 15 miles per hour.     ANSWER