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Linear Equations — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsLinear Equations4 Marks
Question
The distance between two stations is 300km. Two motorcyclists start simultaneously from these stations and move towards each other. The speed of one of them is 7km/ h more than that of the other. If the distance between them after 2 hours of their start is 34km, find the speed of each motorcyclist. Check your solution.
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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 ⇒ 300 - (2x + 2x + 14) = 34 ⇒ 300 - 4x - 14 = 34 286 - 4x = 34 ⇒ 286 - 34 = 4x ⇒ 252 = 4x $\Rightarrow\text{x} = \frac{252}{4} = 63$ Therefore, the speed of the first motorcyclist is 63km/ h.The speed of the second motorcyclist is (x + 7) = (63 + 7) = 70km/ h.Check:
The distance covered by the first motorcyclist in 2 hours = 63 × 2 = 126km The distance covered by the second motorcyclist in 2 hours = 70 × 2 = 140km The distance between the motorcyclists after 2 hours = 300 - (126 + 140) = 34km (which is the same as given) Therefore, the speeds of the motorcyclists are 63km/h and 70km/h, respectively.

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