A man cover a certain distance at some speed .had he move 2 km/h. faster , he would have taken 10 minutes less if he had move 4 km/hr. slower, he would have taken 40 minutes more .Find the distance.
Time = distance / speed = x / y
Let distance = x km
Usual speed = y km/h.
Equation for faster speed
x/y - x/y + 2 = 1 / 6
= x ( y + 2) - xy / y( y + 2) = 1 / 6
= xy + 2x - xy / y( y + 2) = 1 / 6
= 2x / y( y + 2) = 1 / 6
= 12x = y( y + 2)........(1)
Equation for slower speed
x/(y - 4) - x/y = 2 / 3
= xy - x ( y - 4) / y( y - 4) = 2 / 3
= (xy - xy + 4x ) / y( y - 4) = 2 / 3
= 4x / y( y - 4) = 2 / 3
= 12x = y( y - 4)........(2)
Now divide the equation (1) with (2)
12/12 = ( y + 2) / ( y - 4)
1/1 = ( y + 2) / ( y - 4)
1y - 4 = 1y + 2
1y - 1y = 2 + 4
0y = 6
y = 1 / 0
putting the value of y in equation (1)
12x = 1 / 0( 1 / 0 + 2)
x = 0.25 km
Distanc is 0.25 km