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A large truck, traveling $30$ miles per hour, carries a letter from the central post office to the local post office. The letter is then loaded onto a local vehicle, which travels at an average speed of $10$ miles per hour, until the letter reaches its destination. The large truck carried the letter for $a$ minutes and the local vehicle carried the letter for $b$ minutes. If the total distance that the letter travelled from the central post office to its destination was $24$ miles, which of the following equations correctly relates $a$ and $b$ ?$\newline$Choose $1$ answer:$\newline$(A) $\frac{30}{60} a+\frac{10}{60} b=24$$\newline$(B) $\frac{60}{30} a+\frac{60}{10} b=24$$\newline$(C) $30 a+10 b=24$$\newline$(D) $60 \cdot 30 a+60 \cdot 10 b=24$