Question

A man covers a certain distance by his own car. Had he moved 6 km/ h faster he would have
taken 4 hours less. If he had moved 4 km/h solver, he would have taken 4 hours more. The
distance (in km) is:
(A) 240 km
(B) 640 km
(C) 480 km
(D) none of these​

Answer 1

Step-by-step explanation:

Let the speed of car be x and the time taken to cover distance be y.

Hence,distance=speed×time

=xy

Case 1st :

speed=(x+6)km/hr

time=(y-4)hr

Distance =(x+6)(y-4)

=x(y-4)+6(y-4)

=xy-4x+6y-24

But,we have

Distance=xy

or,xy=xy-4x+6y-24

or,xy-4x+6y-24-xy=0

or,-4x+6y-24=0........(1)

case 2nd

speed=(x-4)km/hr

time=(y+4)hr

on doing same as we have done in Case 1st

xy=(x-4)(y+4)

or,xy=xy-4y+4x-16

or,xy-4y+4x-16-xy=0

or, 4x-4y-16=0.....(2)

Adding eq.1and 2

-4x+6y-24+4x-4y-16=0

0r,2y-40=0

or,y=40/2

=20

putting the value of y in eq.1

-4x +6y-24=0

or,-4x+6×20-24=0

or,-4x+120-24=0

or,-4x+96=0

or,-4x=-96

or,x=96/4

=24

Distance=xy

=24×20=480km

Answer 2

Answer:

(C) 480 km

Step-by-step explanation:

Let speed = v and time = t

There are three cases:

d = vt = (v + 6)(t - 4) = (v - 4)(t + 4)

Solving, we get:

v = 24, t = 20.

Therefore,

d = vt = 24*20 = 480 km.