Question

aman riding a cycle covers a distance of 60 km in the direction of wind and comes back to the original place in 8 hours, if the speed of the wind is 10 km/hrs. find the speed of the cycle

Answer 1

let the cycle speed of the Aman = x km/h
distance covered in one direction = d = 60km
speed of the wind = 10 km/hr
total time taken = 8 hr

1) when Aman riding wind direction
relative speed = s1 = (x+10) km/hr
d= 60km
t1 = d/s1
t1= 60/(x+10) ---(1)

2) when Aman riding opposite to wind direction

relative speed = s2= (x-10) km/hr
d= 60km
t2 = 60/(x-10) hr---(2)

given
t1+t2 =8 hr

60 /(x+10 ) + 60/(x-10) = 8

60[ 1/(x+10) + 1/ (x-10) ]= 8

60 [ (x-10+x+10)/(x² - 10²)]= 8
60(2x) = 8(x²-100)
120x/8 = x²-100
15x = x²-100
x²-15x-100=0
⇒x² -20x+5x -100=0
⇒x(x-20)+5(x-20)=0
(x-20)(x+5) =0
x-20 =0 or x+5=0
x=20 or x= -5
x should not be negative
therefore x= 20
cycle speed of Aman = x= 20km/hr