**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

(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

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.

you are very correct dude!!!

Even i was confused by the answer of puzzle.

Maths did its job.. good work .

Distance / Time = speed

So

5(X+Y) = 1

7(X-Y) = 7

12X = 2

x = 1/6 {Speed}

Time = 6 Minutes

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

can you please clearly explain

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

ADDING 2 EQUATIONS

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

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.

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