On a particular day, the wind added 2 miles per hour to Alfonso's rate when he was cycling with the wind and subtracted 2 miles per hour from his rate on his return trip. Alfonso found that in the same amount of time he could cycle 45 miles with the wind, he could go only 33 miles against the wind. What is his normal bicycling speed with no wind?

Question

Mathematics

Cullen Morgan

8 July, 22:59

On a particular day, the wind added 2 miles per hour to Alfonso's rate when he was cycling with the wind and subtracted 2 miles per hour from his rate on his return trip. Alfonso found that in the same amount of time he could cycle 45 miles with the wind, he could go only 33 miles against the wind. What is his normal bicycling speed with no wind?

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Answers (1)

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Tony Horton · Answer 1

Let the normal bicycling speed with no wind = x mph

So, speed with the wind = (x+2) mph

and speed against the wind = (x-2) mph

It means

Time taken in going with the wind = Distance/speed = 45 / (x+2) hours

and

Time taken in going against the wind = 33 / (x-2) hours

And Both times are same, according to the question

So

45 / (x+2) = 33 / (x-2)

On cross multiplying, we get

45 (x-2) = 33 (x+2)

45x-90 = 33x+66

Add 90 to both sides

45x - 90 + 90 = 33x + 66 + 90

45x = 33x + 156

Subtract 33x from both sides

45x - 33x = 33x - 33x + 156

12x = 156

Divide both sides by 12

x = 13

That implies

The normal bicycling speed = 13 Miles per hour