Question

Q14. 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 4hrs 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

Solution :-

Let us assume that speed of ship is v km/hr.

Let us assume that length of journey is x km.

Let us assume that time taken by ship to complete journey is t hr.

It is given that,

Ship covers a certain distance at a uniform speed.

Distance = Speed × Time

x = vt km                     . . . . Equation (1)

Now, it is given that,

If the speed of the ship would have been 6 km/hr faster, it would have taken 4 hrs less than the scheduled time.

Distance = Speed × Time

x = (v + 6) × (t - 4) km

From Equation (1),

vt km = (v + 6) × (t - 4) km

vt = vt - 4v + 6t - 24

6t - 4v = vt - vt + 24

6t - 4v = 24               . . . . Equation (2)            

Now, it is also given that,

If the speed of the ship would have been 6 km/hr slower, it would have taken 6 hrs more than the scheduled time.

Distance = Speed × Time

x = (v - 6) × (t + 6) km

From Equation (1),

vt km = (v - 6) × (t + 6) km

vt = vt + 6v - 6t - 36

6v - 6t = vt - vt + 36

6v - 6t = 36              . . . . Equation (3)

Adding Equation (2) and Equation (3),

(6t - 4v) + (6v - 6t) = 24 + 36

(6v - 4v) + (6t - 6t) = 60

2v + 0 = 60

v = 30

So, speed of ship is 30 km/hr.

Substituting value of 'v' in Equation (2),

6t - 4v = 24

6t - 4(30) = 24

6t - 120 = 24

6t = 24 + 120

t = 24

So, time taken by ship to complete journey is 24 hr.

Substituting value of 'v' and 't' in Equation (1),

x = vt km  

x = 30 × 24 km

x = 720 km

Answer :-

So, the length of journey covered by ship is 720 km.

Answer 2

Answer:

ANSWER-;

Let the actual speed of the train be x km/hr and the actual time taken be y hours. Then,

Distance covered =(xy)km ..(i) [∴ Distance = Speed × Time]

If the speed is increased by 6 km/hr, then time of journey is reduced by 4 hours i.e., when speed is (x+6)km/hr, time of journey is (y−4) hours.

∴ Distance covered =(x+6)(y−4)

⇒xy=(x+6)(y−4) [Using (i)]

⇒−4x+6y−24=0

⇒−2x+3y−12=0 ..(ii)

When the speed is reduced by 6 km/hr, then the time of journey is increased by 6 hours i.e., when speed is (x−6) km/hr, time of journey is (y−6) hours.

∴ Distance covered =(x−6)(y+6)

⇒xy=(x−6)(y+6) [Using (i)]

⇒6x−6y−36=0

⇒x−y−6=0 (iii)

Thus, we obtain the following system of equations:

−2x+3y−12=0

x−y−6=0

By using cross-multiplication, we have,

⇒

$\frac{x}{3 \times - 6 - ( - 1) \times - 12}$

$\frac{y}{ - 2 \times - 6 - 1 \times - 12}$

$\frac{1}{ - 2 \times - 1 - 1 \times 3}$

⇒

$\frac{x}{ - 30} = \frac{ - y}{24} = \frac{1}{ - 1}$

Putting the values of x and y in equation (i), we obtain,

Distance =(30×24)km =720km.

Hence, the length of the journey is 720km.