A train covers a certain distance. If it would have been 5kmph more, then it would have saved 20 minutes. If it would have been 20kmph slower, it would have reached 2 hours later. Find the speed of the train.
Answers
Answer:
Step-by-step explanation:
S=ut
(S=distance, u=velocity and t=time)
2. S=(u+10)(t-2)
(If Speed is 10kmph more, time is 2 hours less)
3. S=(u-10)(t+3)
(If Speed is 10kmph less, time taken is 3 hours more)
Solve (2) and (3) to get t=12 and u=50
S therefore is ut or 50*12 = 600
600km is the answer.
Step-by-step explanation:
Let the original speed be x km/h
Let the distance be d km
time=d/x
Case 1:
speed=x+5
Time= d/(x+5)
according to the statement:
d/x - d/(x+5)= 20 min
(dX +5d - dX)/(x^2 +5x)= 1/3 hr
5d=(x^2+5x)/3
15d=x^2 + 5x
x^2=15d-5x----------------- (equation 1)
case 2:
speed= x-20
time= d/(x-20)
according to the statement:
d/(x-20)-d/x=2 hrs
(dx-dx+20d)/(x^2-20x)= 2
On solving we get
20d= 2x^2-40x
divide by 2
10d= x^2-20x
x^2= 10d + 20x-------------(equation 2)
from equation 1 and 2
15d-5x=10d+20x
5d=25x
d=5x
substitute this value in any of the equation.
equation 1: x^2=15d-5x
x^2= 15*5x - 5x. ( from the above value)
x^2= 75x-5x
x^2=70x
divide by x
x=70 km/hr
d= 5x
d= 350km.
hence the speed of the train is 70km/hr.