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Answers
Answer:
Let x=train speed
Let y = car speed
speed = distance / time
time = distance / speed
6 hours 30 minutes = 6.5 hours <== 400 km by train ; 200 km by car
1/2 hour longer = 7 hours <== 200 km by train ; 400 km by car
Train time + car time = total time
400 / x + 200 / y = 6.5 <== two equations and two unknowns
200 / x + 400 / y = 7 . . . . . . solve for x and y
400y + 200x = 6.5 xy
200y + 400x = 7 xy
400y - 6.5 xy = - 200x
200y - 7xy = - 400x
y ( 400 - 6.5x) = -200x
y ( 200 - 7x) = -400x
y (6.5x - 400) = 200x
y (7x - 200) = 400x
y = 200x / (6.5x - 400)
y = 400x / (7x - 200) . . . note this equation ... for later use
. . . since both equal y, the difference is zero
200x / (6.5x - 400) - 400x / (7x - 200) = 0
200x ( 7x - 200) - 400x (6.5x - 400) = 0
1400x^2 - 40000x - 2600x^2 + 160000x = 0
120000 x - 1200 x^2 = 0
100 - x = 0
x = 100 km / h ( trains speed )
y = 400x / (7x - 200) . . . see note above
y = 400 * 100 / (7 * 100 - 200)
y = 80 km / h ( car speed)
hope this helps
Answer : Hence, the speed of the train is 100km/hr and the speed of the car is 80km/hr.
Step by step Explantation : Let the speed of a train =xkm/hr
And the speed of a car =ykm/hr
Total distance travelled =600km
According to the question,
If he covers 400km by train and rest by car i.e. (600−400) =200km
Time take =6 hrs 30min =6+ 60 30 =6.5 hrs
If he travels 200km by train and rest by car i.e. (600−200) =400km
He takes half hour longer i.e. 7 hours
So, total time = train time + car time We know that, time = speed distance ⇒ x 400 + y 200 =6.5…
(i) ⇒ x 200 + y 400 =7…
(ii) Let take x 1 = u and y 1 =v 400u+200v=6.5⋯
(iii) and 200u+400v=7…
(iv) On multiplying Eq.
(iii) by 2 and Eq.
(iv) by 4, we get 800u+400v=13…
(a) 800u+1600v=28…
(b) On subtracting Eq.(a) from Eq. (b), we get 800u+1600v−800u−400v=28−13 ⇒1200v=15 ⇒v= 1200 15 ⇒v= 80 1
On putting the value of v in Eq. (iv), we get 200u+400( 80 1 )=7 ⇒200u+5=7 ⇒200u=2 ⇒u= 100 1 So, we get u= 100 1 and v= 80 1 ⇒x=100 and y=80
Hence, the speed of the train is 100km/hr and the speed of the car is 80km/hr.
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