Respuesta :
Let Alfonso's normal bicycling speed with no wind be designates [tex] S [/tex].
Since the Time is common to both the cases of "with the wind" and "against the wind", let it be designated as [tex] T [/tex].
Now, we know that "with the wind" Alfonso travels 57 miles in time, T and "against the wind" he travels 33 miles in the same time.
Also, since the speed of the wind is a constant 4miles per hour, we know that "with the wind" Alfonso's actual speed will be [tex] (S+4) [/tex] miles per hour and "against the wind" his speed will be [tex] (S-4) [/tex] miles per hour.
With all the information that is required let us proceed with the solution to the question. This will involve a formula which connects, actual speed, distance travelled and time taken to travel that distance. That formula is:
Distance=Actual Speed x Time Taken
Thus, in our question, the above equation for the two cases will be as:
For "with the wind"
[tex] (S+4)\times T=57 [/tex]
For "against the wind"
[tex] (S-4)\times T=33 [/tex]
Now, expressing [tex] T [/tex], in both the equations, in terms of the other parameters, we get:
[tex] T=\frac{57}{S+4} [/tex] (from the "with the wind" condition) and
[tex] T=\frac{33}{S-4} [/tex] (from the "against the wind" condition)
Since [tex] T [/tex] is the same in both the cases, we may equate the two equations to get:
[tex] \frac{57}{S+4}=\frac{33}{S-4} [/tex]
which after basic simplification yields:
[tex] 11S+44=19S-76 [/tex]
[tex] 8S=120 [/tex]
[tex] \therefore S=15 [/tex]
Thus, Alfonso's normal bicycling speed with no wind is 15 miles per hour.
