A train travels at a certain average speed for a distance of 63 km and then travels at a distance of 72 km at an average speed of 6 km/hr more than its original speed. If it takes 3 hours to complete total journey, what is the original average speed ?
Answers
Answered by
2
Solutions :-
We know,
Distance = Speed × time
Speed = distance/time
Time = distance/speed
We have,
Distance travels on certain speed = 63 km
Let Original speed of train be x
Distance travels at speed of 6 km/hr = 72 km
Speed = (x + 6) km per hour
Time = 72/(x+6) hrs
Total journey completed in 3 hrs
Find the value of x :-
A/q
=> 63/x + 72/(x + 6) = 3
=> 63(x + 6) + 72x = 3x(x+ 6)
=> 21(x + 6) + 24x = x(x+6)
=> 45x + 21×6 = x2 + 6x
=> x^2 - 39x - 126 = 0
=> x^2 - 39x - 126 = 0
=> x^2-42x+3x -126=0
=> x(x-42)+3(x-42)=0
=> (x - 42)(x + 3) = 0
=> x = 42 or x = -3
Answer : Original average speed = 42 km per hr
Note :- Distance is always in positive
We know,
Distance = Speed × time
Speed = distance/time
Time = distance/speed
We have,
Distance travels on certain speed = 63 km
Let Original speed of train be x
Distance travels at speed of 6 km/hr = 72 km
Speed = (x + 6) km per hour
Time = 72/(x+6) hrs
Total journey completed in 3 hrs
Find the value of x :-
A/q
=> 63/x + 72/(x + 6) = 3
=> 63(x + 6) + 72x = 3x(x+ 6)
=> 21(x + 6) + 24x = x(x+6)
=> 45x + 21×6 = x2 + 6x
=> x^2 - 39x - 126 = 0
=> x^2 - 39x - 126 = 0
=> x^2-42x+3x -126=0
=> x(x-42)+3(x-42)=0
=> (x - 42)(x + 3) = 0
=> x = 42 or x = -3
Answer : Original average speed = 42 km per hr
Note :- Distance is always in positive
Answered by
2
Answer:
Step-by-step explanation:
Let the speed of the train be X km/ h
with speed 'x' travelled distance = 63km
Time taken to travelled distance=63/X
Remaining distance travelled with speed(X+6)
Travelled distance =72 km
Time taken to travel 72km=72/X+6
Total time taken to travel distance=3 hour
Therefore,63/x +72/x+6 =3
63(x+6)+72x =3x^2+18x
x^2-39x-126=0
x^2-42x+3x-126=0
X(x-42)+3(x-42)=0
X=42,x=-3
X can't be negative
Therefore ,speed of a train=42km/h
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