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. What is his normal bicycling speed with no wind?
a. 15 km/h c. 35 km/h
b. 40 km/h d. 45 km/h

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.  What is his normal bicycling speed with no wind?
a. 15 km/h c. 35 km/h 
b. 40 km/h d. 45 km/h

anonymous · Answer

the general equation for this is
Distance = Rate x Time

Let Alfonso's normal biking speed = R and let T be the length of time in the problem
36.5=(R+3) x T
24=(R-3) x T

solve for R

aravindg · Answer

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anonymous · Answer

As the question stands, none of the multiple choice answers are correct.
Answer A is close, but the answer is not exactly a nice number.
For answer A to be correct, instead of being able to cycle 36.5 km in the length of time, Alfonso should only be able to cycle 36 km.

anonymous · Answer

@Peter14
I dont know how to solve further for R in the equations mentioned at the top

anonymous · Answer

@ganeshie8 
@mathmate

mathmate · Answer

@peter14  has already set up the equations:

36.5=(R+3) x T
24=(R-3) x T
You will need to solve for R.
To do this, you would divide one equation by the other to eliminate T.
36.5/24 = (R+3)/(R-3)
Cross multiply to get
36.5(R-3)=24(R+3)
Expand and solve for R.

As Peter said, it will be a not nice number, but close to 15 km/h.
There is probably a typo in either the question or the answers.

anonymous · Answer

okay 
thanks

mathmate · Answer

You're welcome!   :)

anonymous · Answer

hahaaa
maimi girl.....
coincidently @jaikid_077 and i had the same question

mathmate · Answer

ok, that explains it!  :)

anonymous · Answer

good question though...lol

mathmate · Answer

:) talk to you some other time!