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Linear Equations — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSLinear Equations5 Marks
Question
The distance between two stations is $300\ km$. Two motorcyclists start simultaneously from these stations and move towards each other. The speed of one of them is $7\ km/ h$ more than that of the other. If the distance between them after $2$ hours of their start is $34\ km$, find the speed of each motorcyclist. Check your solution.
✓

Answer

Let the speed of one motorcyclist be $x \ km/ h.$
So, the speed of the other motorcyclist will be $(x + 7)\ km/ h.$
Distance travelled by the first motorcyclist in $2$ hours $= 2x \ km$
Distance travelled by the second motorcyclist in $2$ hours $= 2(x + 7)\ km$
Therefore, $300 - (2x + (2x + 14)) = 34 $
$\Rightarrow 300 - (2x + 2x + 14) = 34 $
$\Rightarrow 300 - 4x - 14 = 34 286 - 4x = 34$
$\Rightarrow 286 - 34 = 4x$
$ \Rightarrow 252 = 4x$
$\Rightarrow\text{x} = \frac{252}{4} = 63$
Therefore, the speed of the first motorcyclist is $63\ km/ h.$
The speed of the second motorcyclist is $(x + 7) = (63 + 7) = 70\ km/ h$.
Check:
The distance covered by the first motorcyclist in $2$ hours $= 63 \times 2 = 126\ km$
The distance covered by the second motorcyclist in $2$ hours $= 70 \times 2 = 140\ km$
The distance between the motorcyclists after $2$ hours $= 300 - (126 + 140) = 34\ km$ (which is the same as given)
 Therefore, the speeds of the motorcyclists are $63\ km/h$ and $70\ km/h$, respectively.

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