Question

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

Answer 1

$\textsf{Let the Uniform Speed of the Ship be : S km per hour}$

$\textsf{Let the Time taken to complete the Entire Journey be : T hours}$

$\bigstar\;\;\;\textsf{We know that : \boxed{\mathsf{Distance\;traveled = Speed \times Time\;taken}}}$

$\mathsf{\implies Distance\;traveled\;by\;Ship = (S \times T)\;km}$

$\textsf{Given : If the Speed of Ship would have been 6 km per hour faster, it would}\\\textsf{have taken 4 hours less than the scheduled time.}$

$\implies \textsf{The Speed of the Ship would be : (S + 6) km per hour}$

$\implies \textsf{Time taken by Ship to complete the journey would be : (T - 4) hours}$

$\implies \mathsf{Distance\;traveled = (S + 6) \times (T - 4)\;km}$

$\mathsf{But,\;We\;found\;that : Distance\;traveled = (S \times T)\;km}$

$\implies \mathsf{(S \times T) = (S + 6) \times (T - 4)}$

$\implies \mathsf{ST = ST - 4S + 6T - 24}$

$\implies \mathsf{6T - 4S = 24\;------\;[1]}$

$\textsf{Given : If the Speed of Ship would have been 6 km per hour slower, it would}\\\textsf{have taken 6 hours more than the scheduled time.}$

$\implies \textsf{The Speed of the Ship would be : (S - 6) km per hour}$

$\implies \textsf{Time taken by Ship to complete the journey would be : (T + 6) hours}$

$\implies \mathsf{Distance\;traveled = (S - 6) \times (T + 6)\;km}$

$\implies \mathsf{(S \times T) = (S - 6) \times (T + 6)}$

$\implies \mathsf{ST = ST + 6S - 6T - 36}$

$\implies \mathsf{6S - 6T = 36\;------\;[2]}$

$\textsf{Adding both Equations [1] and [2], We get :}$

$\implies \mathsf{(6T - 4S) + (6S - 6T) = 24 + 36}$

$\implies \mathsf{6T - 6T + 6S - 4S = 60}$

$\implies \mathsf{2S= 60}$

$\implies \mathsf{S= 30}$

$\textsf{Substituting S = 30 in Equation [1], We get :}$

$\implies \mathsf{6T - 4(30) = 24}$

$\implies \mathsf{6T - 120 = 24}$

$\implies \mathsf{6T = 144}$

$\implies \mathsf{T = 24}$

$\implies \textsf{Speed of the Ship = 30 km per hour}$

$\implies \textsf{Time taken by the Ship to cover the Entire Journey = 24 hours}$

$\implies \mathsf{Distance\;traveled\;by\;the\;Ship = (30 \times 24)\;km}$

$\implies \mathsf{Distance\;traveled\;by\;the\;Ship = 720\;km}$

$\underline{\bf{Answer}} : \textsf{The Length of the Journey = 720 km}$

Answer 2

Answer:

720 km

Step-by-step explanation:

Let say time of journey =  t hr

Let say uniform speed = s km/hr

Length of journey = st  km

Increased speed = s + 6 km/hr

Time with increased speed = t - 4

Distance travelled = (s+6)(t-4)

(s+6)(t-4) = st

st + 6t - 4s - 24 = st

6t = 4s + 24

Slower speed = s- 6 km /hr

Time taken with slower speed = t+6

Distance Traveled = (s-6)(t+6)

(s-6)(t+6) = st

st -6t +6s -36 = st

6t = 6s -36

equating both equation

6s -36 = 4s + 24

2s = 60

s = 30 km/hr

6t = 4s + 24

6t = 120 + 24

6t = 144

t = 24 hr

Distance ( length of journey) = 30 * 24 = 720 km