Question

If vinay had walked 2 km/hr. faster, he would have taken 10 min less to walk 4 km. what is vinay's speed of walking?
a) 7km/hr
b) 5 km/hr
c) 4 km/hr
d) 6 km/hr

Answer 1

Sᴏʟᴜᴛɪᴏɴ :-

Let us Assume That, initial Speed of vinay was x km/h.

Than,

→ Distance = 4km

→ Speed = x km/h.

→ Time = (D/S) = (4/x) Hours.

Now ,

→ Distance = 4km

→ Speed = (x+2) km/h.

→ Time = (D/S) = 4/(x+2) Hours.

Given That, he Takes 10 min . Less .

So,

→ (4/x) - 4/(x + 2) = 10 min = (10/60) = 1/6 Hours .

→[ 4(x+2) - 4x] /x(x + 2) = 1/6

→ x² + 2x = 48

→ x² + 2x - 48 = 0

→ x² + 8x - 6x - 48 = 0

→ x(x + 8) - 6(x - 8) = 0

→ (x + 8)(x - 6) = 0

→ x = (-8) or 6 . [ Speed in -ve ≠ ] .

Hence, vinay's speed of walking is 6km/h. (Option D).

Answer 2

Solution:

Let the walking speed of Vinay = x

Distance = 4km

Time taken = 4/x

In the second case,

→ speed is = x+2

→ time taken = 4/x+2

It is given that he would have taken 10min less to walk 4km

→4/x+2 = 4/x+1/6

→4/x+2 -4/x=1/6

→{4(x)-4(x+2)}/x(x+2) = 1/6

→4x-4x-8/x(x+2)=1/6

→8/x(x+2) = 1/6

→8 × 6= x²+2x

→48=x²+2x

→x² +2x- 48=0

by discriminant formula

→x=[-b±√(b²-4ac)]/2a

→x=[-2±√4+192]/2

→x=-2±√196/2

→x=(-2±14)/2

→x=(-2+14)/2. x=(-2-14)/2

→x=12/2. x=-16/2

→x=6. x=-8

therefore vinay's speed of walking is 6km