# Riding Against the Wind Puzzle

Problem: A horse rider went a mile in 5 minutes with the wind and returned in 7 minutes against the wind. How fast could he ride a mile if there was no wind?

Solution:

Most of us will proceed like that if a rider goes a mile in 2 minutes with the wind, and returns against the wind in 3 minutes, that 2 and 3 equal 5, should give a correct average, so that time taken should be two and half minutes. We find this answer to be incorrect, because the wind has helped him for only 2 minutes, while it has worked adversely for 3 minutes.

If he could ride a mile in 2 minutes with the wind, it is clear that he could go a 1.5 mile 3 minutes, and 1 mile in 3 minutes against the wind.

Therefore 2.5 miles in 6 minutes gives his actual speed, because the wind helped him just as much as it has retarded him, so his actual speed for a single mile without any wind would be (2.5)/6 = 5/12 miles/sec

### 0 Thoughts on “Riding Against the Wind Puzzle”

1. (H+w) *5=(H-W)*7=1 w is speed of wind and h is speed of horse gives speed of horse H=6/35 therefore answer is 6/35 miles per minute

• Rishabh kumar gaur on September 2, 2015 at 9:58 am said:

nice work dude…..hats off…

• And to complete the answer, given that the question is “How fast could he ride a mile if there was no wind?”, we must invert that (because time = 1 mile / speed), to get 35/6 minutes, which is 5 minutes and 50 seconds.

• shivam shukla on May 29, 2016 at 10:37 am said:

you are very correct dude!!!
Even i was confused by the answer of puzzle.
Maths did its job.. good work .

2. Nitin Gupta on April 28, 2015 at 12:19 pm said:

Distance / Time = speed
So
5(X+Y) = 1
7(X-Y) = 7
12X = 2
x = 1/6 {Speed}
Time = 6 Minutes

3. Sumit Sharma on May 12, 2015 at 4:17 am said:

1/r + 1/w=5/60

1/r – 1/w=7/60

2/r=12/60

r/2=60/12 r=60*2/12= 10 miles /hr

r=rider, w=wind

4. harshitha on June 23, 2015 at 7:38 pm said:

can you please clearly explain

• Nitik on July 30, 2015 at 2:53 am said:

Rider rides 1 mile in 5 min with wind
=> speed with wind = 1/5 miles per min
i.e R + W = 1/5 equation 1
Rider rides 1 mile in 7 min against wind
=> speed against wind = 1/7 miles per min
i.e R – W = 1/7 equation 2

R + W = 1/5 where : R = speed of rider
+ W = speed of wind
R – W = 1/7
=> 2R = 12/35
hence R = 6/35 miles/min

5. Horse speed with the wind = 1mile in 5 minutes.
So he was going 1/5 miles per minute.

Horse speed against the wind = 1 mile in 7 minutes.
So he was going 1/7 miles per minute.

average of speeds = ( 1/5 + 1/7 ) รท 2 = 6/35 miles per minute.

6. a. W+H = 12 Miles/Hr (Since 5 minutes/mile with wind; 12 *5 = 60)
b. H-W = 8.57 Miles/Hr (Since 7 minutes/mile against wind; 8.57 * 7 = 60)

a+b = 2H = (12+8.57) Miles/Hr
= 2H = 20.57 Mi/Hr
= H = 10.285 Mi/Hr

and 1 mile would take 60 min/10.285 Miles = 5.8337 min; or 5 min 50 seconds