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Linear Equations in One Variable — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSLinear Equations in One Variable5 Marks
Question
The distance between two stations is $340\ km$. Two trains start simultaneously from these stations on parallel tracks to cross each other. The speed of one of them is greater than that of the other by $5\ km/ hr$. If the distance between the two trains after $2$ hours of their start is $30\ km$, find the speed of each train.
✓

Answer

Distance between two stations $= 340\ km.$
Let the speed of the first train $= x\ km/ hr.$
Then speed of second train $= (x + 5)\ km/ h.$
Time $= 2$ hours Distance travelled by the first train in $2$ hours =$ 2x\  km$ and
distance travelled by the first trian in $2$ hours $= 2(x + 5)\ km$
According to the condition, $340 - [2(x + 5) + 2x] = 30km$
$\Rightarrow 340 - (2x + 10 + 2x) = 30 $
$\Rightarrow 4x + 10 = 340 - 30 $
$\Rightarrow 4x = 340 - 30 - 10$
$ \Rightarrow 4x = 300$
$\Rightarrow\text{x}=\frac{300}{4}=75$
$\therefore$ Speed of first train $= 75\ km/ hr$ and speed of second train $= 75 + 5 = 80\ km/ hr$

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