Two cars C and D start from a junction along two...

Two cars $C$ and $D$ start from a junction along two perpendicular roads at $8: 00$ a.m. and $9: 00$ a.m. respectively. If at 12 noon, the cars, which travel at the same speed, are $150 \mathrm{~km}$ apart, then, find the speed of each car. (A) $15 \mathrm{kmph}$ (B) $45 \mathrm{kmph}$ (C) $60 \mathrm{kmph}$ (D) $30 \mathrm{kmph}$

Two cars $C$ and $D$ start from a junction along two perpendicular roads at $8: 00$ a.m. and $9: 00$ a.m. respectively. If at 12 noon, the cars, which travel at the same speed, are $150 \mathrm{~km}$ apart, then, find the speed of each car.
(A) $15 \mathrm{kmph}$
(B) $45 \mathrm{kmph}$
(C) $60 \mathrm{kmph}$
(D) $30 \mathrm{kmph}$

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Key Concepts

Right Triangle and the Pythagorean Theorem

When motion occurs along two perpendicular directions, the overall displacement from the starting point can be found by treating the path as the legs of a right triangle. The Pythagorean theorem is then applied to determine the length of the hypotenuse, which represents the total displacement, by using the squares of the individual distances along each leg.

Uniform Motion

Uniform motion refers to movement in which an object travels at a constant speed. This principle simplifies analysis because the relationship between distance, speed, and time remains linear, allowing for the calculation of any of these variables when the other two are known.

Distance-Speed-Time Relationship

This concept involves understanding that distance traveled is the product of speed and time. It is foundational in solving problems that deal with uniform motion, where the distance covered, the speed at which an object moves, and the time taken are directly related by the equation distance = speed × time.

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