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
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
(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