Physics, asked by piyushingh6442, 11 months ago

A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. Find the speed of the train.

Answers

Answered by Anonymous
16

answer:

40kmh

Explanation:

Total Distance S = 480km

Formula For Speed

speed = distancetime

Hence distance = speed × time

Case-i

let the uniform speed of Train = vkmh

and the time taken to complete distance = (t) hour

Distance S = speed × time = vt. . . . (equation 1)

Case-II

If speed has been 8km / h less then train would have taken 3 hours more to cover the same distance.

Now in this situation

speed of train = (v − 8) kmh

and Time taken to complete distance = (t + 3) hour

Distance S = speed × time = (v − 8) (t + 3). . . . . (equation 2)

Since distance for both cases are same.

Comparing equation 1 and equation 2, we get

⇒vt = (v − 8) (t + 3)

⇒vt = (v) (t + 3) −8 (t + 3) = vt + 3v − 8t − 24

cancel vt from both side

⇒0=3v−8t−24

⇒3v−8t=24

⇒3v=24+8t

⇒v=24+8t3

but from equation 1 the value of t=Sv=480v(hour)

⇒3v=24+8(480v)

⇒3v2=24v+3840

⇒3v2−24v−3840=0

⇒v2−8v−1280=0

factorize the quadratic equation

⇒(v−40)(v+32)=0

v is either 40kmh or −32kmh

Speed is Positive hence 

Speed=40kmh

Answered by Anonymous
205

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(i) Let us consider,

The breadth of the rectangular plot is x m.

Thus, the length of the plot = (2x + 1) m

As we know,

Area of rectangle = length × breadth = 528 m2

Putting the value of length and breadth of the plot in the formula, we get,

(2x + 1) × x = 528

⇒ 2x^2 + x = 528

⇒ 2x^2 + x – 528 = 0

Hence, 2x2 + x – 528 = 0, is the required equation which represents the given situation.

(ii) Let us consider,

speed of train = x km/h

And

Time taken to travel 480 km = 480 (x) km/h

As per second situation, the speed of train = (x – 8) km/h

As given, the train will take 3 hours more to cover the same distance.

Therefore, time taken to travel 480 km = (480/x) + 3 km/h

As we know,

Speed × Time = Distance

Therefore,

(x – 8)[(480/x) + 3] = 480

⇒ 480 + 3x – (3840/x) – 24 = 480

⇒ 3x – (3840/x) = 24

⇒ 3x^2 – 24x – 3840 = 0

⇒ x^2 – 8x – 1280 = 0

Hence, x^2 – 8x – 1280 = 0 is the required representation of the problem mathematically

Hope it's Helpful.....:)

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