Question

A ship covered a certain distance at a uniform speed.If the speed of the ship would have been 6km/hr faster,it would have taken 4 hours less than the scheduled time,and if the speed of the ship were slower than 6km/hr,it would have taken 6 hours more than the scheduled time .Find the length of the journey.

Answer 1

let the speed of the ship be x km/hr and time taken by it be t hrs. distance be l km/hr.
we know that speed=distance/time now distance=speed×time
l=x×t_______(1)
1st condition l=(x+6)(t-4)
now putting the value of l from eqn1
xt=xt-4x+6t-24
6t-4x=24_________(3)
2nd condition l=(x-6)(t+4)
now putting the value of l from eqn1 we get
xt=xt+4x-6t-24
4x-6t=24_________(4)
now from eqn3 we get t=24+4x/6
now putting in eqn 4 we get
4x-6 (24+4x)/6=24
8x=48
x=6, now t=24+4 (6)/6,t=48/6,t=8
now therefore l=x×t
l=6×8=48km
ANS:-TGEREFORE THE LENGTH OF THE JOURNEY IS 48 KM.

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Answer 2

Answer:

Step-by-step explanation:

Hi ,

Let the speed of the ship = x km / hr

distance covered = d km

time = t1 = d/ x -----( 1 )

1 ) speed of the ship if 6km /h faster = ( x+ 6 ) km/h

time ( t2 ) = d / ( x + 6 ) ------ ( 2 )

t1 - t2 = 4

d/x - d/ ( x + 6 ) = 4

d = ( 2/3 ) [ x ( x + 6 ) ] ----( 3 )

2 ) speed of the ship 6 km / h slower than intial speed = ( x - 6 ) km / h

time = t3 = d / ( x - 6 ) h----( 4 )

t3 - t1 = 6

d/ ( x - 6 ) - d/x = 6

d = x( x - 6 ) ----( 5 )

( 3 ) = ( 5 )

( 2/3 ) [ x ( x + 6 ) ] = x ( x - 6 )

2( x + 6 ) =3 ( x - 6 )

2x + 12 = 3x - 18

12 + 18 = 3x - 2x

x = 30 km/h

put x value in equation ( 5 ) ,

d = x ( x - 6 )

= 30 ( 30 - 6 )

= 30 × 24

= 720 km

I hope this helps you.

:)