Question

On a particular day, the wind added 3 km per hour to Alfonso's rate when he was cycling with the wind and subtracted 3 km per hour from his rate on his return trip. Alfonso found that in the same amount of time he could cycle 36.5 km with the wind, he could go only 24 km against the wind. To the nearest whole number, what is his normal bicycling speed with no wind?

a) 15 km/h
b) 40 km/h
c) 35 km/h
d) 45 km/h

Answer 1

Alfonso's normal bicycling speed with no wind is 15 km/h, which is found by setting up and solving a pair of equations that compares his travel times with and against the wind.

Step-by-step explanation:

To find Alfonso's normal bicycling speed with no wind, we need to establish two equations based on the information provided:

Let x be the normal cycling speed with no wind. When cycling with the wind, his speed is x + 3 km/h, and against the wind, his speed is x - 3 km/h. The time taken for both parts of the trip is the same, so the distances divided by the speeds are equal.

Equation for with the wind:
Time = Distance / Speed = 36.5 / (x + 3)

Equation for against the wind:
Time = Distance / Speed = 24 / (x - 3)

Since the times are equal, we have:
36.5 / (x + 3) = 24 / (x - 3)

By cross-multiplying and solving for x, we find that Alfonso's normal bicycling speed is:

x = 15 km/h

The correct answer to the nearest whole number is:
a) 15 km/h