Question

A ship covered a certain distance at a uniform speed. If the ship was 6km/h faster, it would take 4 hours less than the scheduled time. And if the ship was slower than 6km/h, it would take 6 more hours. How long was the journey?

Points: 15

Answer 1

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.

:)

Answer 2

Let the ship speed be x km/hr.

Let the length of the journey be y km.

We know that Speed = Distance/Time

                        Then Distance = Speed * Time

                                                 = x * y

                                                 = xy.   ------------ (*)

Given that The ship was 6km/hr faster, it would take 4 hours less than the scheduled time.

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

xy - 4x + 6y - 24 = xy

-4x + 6y = 24

2x - 3y = -12   ----------- (1).


Given that If the ship was slower than 6km/hr, it would take 6 more hours.

(x - 6)(y + 6) = xy.

xy + 6x - 6y - 36 = xy

6x - 6y = 36

x - y = 6    ---------- (2)


On solving (1)*3 & (2)*6, we get

6x - 9y = -36

6x - 6y = 36

------------------

      -3y = -72

         y = 72/3

            = 24.   ----------- (3)


Substitute x = 24 in (2), we get

x - y = 6

x - 24 = 6

x = + 24

x = 30.    -------- (4)


Substitute (3) & (4) in (*), we get

The distance covered by the ship = 30 * 24

                                                          = 720km.


Therefore the length of the journey = 720km.


Hope this helps!