SOLUTION: A bicyclist traveling in a flat, open area could ride at 3 times the speed of the wind if the wind were absent. On this day, he traveled 42 miles against the wind in 4 more hours t

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Question 73150This question is from textbook
: A bicyclist traveling in a flat, open area could ride at 3 times the speed of the wind if the wind were absent. On this day, he traveled 42 miles against the wind in 4 more hours than it took to go 4 miles with the wind on the return trip. What is the speed of the bike in no wind? This question is from textbook

Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
Let the speed of wind be 'x' mph.
In absence of wind, the cyclist can travel with a speed 3 times the wind speed i.e. at speed '3x' mph.

While travelling against wind, the effective speed of the cyclist is (3x - x) = '2x' mph
While travelling with the wind, the effective speed of the cyclist is (3x + x) = '4x' mph
Now, SPEED+=+DISTANCE%2FTIME so TIME+=+DISTANCE%2FSPEED.

The distance between the source and destination is 42 miles.
Time reqd. for going from source to destination = TIME+=+DISTANCE%2FSPEED+=+42%2F%282x%29=21%2Fx hrs.
Time reqd. for travelling 4 miles during return journey = TIME+=+DISTANCE%2FSPEED+=+4%2F%284x%29=2%2Fx hrs.
According to the problem, the later time is 4 hours less than the former.

So, 21%2Fx+-+2%2Fx+=+4
or 19%2Fx+=+4
or x+=+19%2F4+=+4.75

The speed of the bike in absence of wind = 3x+=+3%2A4.75+=+14.25 miles per hr.