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
Answers
Answered by
123
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.
:)
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.
:)
Answered by
113
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!
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!
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