13. The distance between two stations A and B is
250 km. Two trains start simultaneously from
A and B in opposite directions. The distance
1
between them after 2 - hours is 25 km. If the
2
speed of one train is 10 km/hr. more than the
other. Find the speed of each of the trains.
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Given :-
To find :-
If the peed of 1 train is 10 km/hr more than other then find speed of both trains .
Solution :-
Let's assume that the speed of train from station A = x km/hr .
So the speed of train from station B = 10+x km/hr
[tex]\Large{\boxed{\rm{Distance = speed \times time } }}\\[/tex]
After two hours the distance covered will be -
[tex]\sf{\implies \; Train \; A = x \times 2 = 2x }\\[/tex]
[tex]\sf{\implies \; Train \; B = [x+10] \times 2 = 2x + 20 }\\[/tex]
Now comparing it with total distance -
[tex]\sf{\implies 2x + 2x + 20 + 25 = 250 }\\[/tex]
[tex]\sf{\implies 4x + 45 = 250 }\\[/tex]
[tex]\sf{\implies 4x = 250 - 45 \rightarrow 205 }\\[/tex]
[tex]\sf{\implies x = \frac{250}{4} \rightarrow 51.25 }\\[/tex]
Speed of train A = 51.25 km/hr
Speed of train B = 61.25 km/hr
Verified answer
✯✯ QUESTION ✯✯
The distance between two stations A and B is 250 km. Two trains start simultaneously from A and B in opposite directions. The distance between them after 2 - hours is 25 km. If the speed of one train is 10 km/hr. more than the other. Find the speed of each of the trains.
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✰✰ ANSWER ✰✰
Let the speed of Train A ➙ y km/hr
As Given that speed of one train is 10km/hr more than other train..So,
Speed of Train B ➙ 10 + y km/hr
☛Distance Covered After Two Hours : -
[tex]\longmapsto\tt{Train (A)=y\times{2}}[/tex]
[tex]\longmapsto\tt{2y}[/tex]
[tex]\longmapsto\tt{Train (B)= (y + 10)\times{2}}[/tex]
[tex]\longmapsto\tt{2y+20}[/tex]
☛A.T.Q : -
[tex]\longmapsto\tt{25+2y+2y+20=250}[/tex]
[tex]\longmapsto\tt{45+4y=250}[/tex]
[tex]\longmapsto\tt{4y=250-45}[/tex]
[tex]\longmapsto\tt{4y=205}[/tex]
[tex]\longmapsto\tt{\cancel\dfrac{205}{4}}[/tex]
[tex]\blue\longmapsto\:\large\underline{\boxed{\bf\tt\red{x}\tt\green{=}\tt\orange{51.25}}}[/tex]
_______________________
[tex]\longmapsto\tt{Speed\:of\:Train\:A=y}[/tex]
[tex]\longmapsto\tt{\large{\boxed{\bold{\bold{\red{\sf{51.25\:km/hr}}}}}}}[/tex]
[tex]\longmapsto\tt{Speed\:of\:Train\:B=10+y}[/tex]
[tex]\longmapsto\tt{10+51.25}[/tex]
[tex]\longmapsto\tt{\large{\boxed{\bold{\bold{\purple{\sf{61.25\:km/hr}}}}}}}[/tex]