Question

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

Answer 1

$\huge{\mathfrak{\red{Question:-}}}$

A car covered a certain distance at a uniform speed. If the car would have been 6km/hr faster, it

would have taken 4 hours less than the required time, and if car were slower by 6km/hr, it woul

have taken 6 hours more than required time. Find the length of the journey.

$\huge{\mathfrak{\green{Answer:-}}}$

Solution :-

Let x km/hr be the speed of train

Let y be the time taken by the train

Distance = speed x time

= x y

To form the first equation let us consider the given information from the question that is If the train had been 6 km/hr faster,it would have taken 4 hours less than the scheduled time.

it clearly says that speed is increased by 6 and time is reduced by 4

So , (x + 6) (y - 4) = x y

x y - 4 x + 6 y - 24 = x y

x y - x y - 4 x + 6 y = 24

- 4 x + 6 y = 24

divided by (-2) => 2 x - 3 y = -12 ----- (1)

To form the second equation let us consider the given information from the question that is If the train were slower by 6km/hr, then it would have taken 6 hours more than the scheduled time.

it clearly says that speed is reduced by 6 and time is increased by 6

So , (x - 6) (y + 6) = x y

x y + 6 x - 6 y - 36 = x y

x y - x y + 6 x - 6 y = 36

6 x - 6 y = 36

divided by (6) => x - y = 6 ----- (2)

2 x - 3 y = -12

(2) x 2 => 2 x - 2 y = 12

(-) (+) (-)

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

- y = -24

y = 24

Now we have to apply the value of y in the first equation to get value of x

Substitute y = 24 in the first equation we get

2 x - 3 (24) = -12

2 x - 72 = -12

2 x = -12 + 72

2 x = 60

x = 60/2

x = 30

Speed of the train = 30 km/hr

Time taken by the train = 24 hours

Distance covered by the train = x y = 30 x 24 = 720 km

Verification:-

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

2 x – 3 y = -12

2(30) - 3(24) = -12

60 - 72 = -12

-12 = -12

#Answer with quality

#Bal