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) $60 \cdot 30 a+60 \cdot 10 b=24$

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Q. 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

Convert to Hours: To find the correct equation, we need to convert the time spent by the truck and the local vehicle into hours since the speeds are given in miles per hour (mph). Since there are $60$ minutes in an hour, we divide the time in minutes by $60$ to convert it to hours.
Calculate Truck Distance: For the large truck traveling at $30 \, \text{mph}$ for $a$ minutes, the distance covered by the truck is $(30 \, \text{miles/hour}) \times (a \, \text{minutes} / 60 \, \text{minutes/hour}) = (30/60)a = (1/2)a \, \text{miles}.$
Calculate Local Vehicle Distance: For the local vehicle traveling at $10$ mph for $b$ minutes, the distance covered by the vehicle is $(10 \text{ miles/hour}) \times (b \text{ minutes} / 60 \text{ minutes/hour}) = (10/60)b = (1/6)b$ miles.
Total Distance Equation: The total distance covered by both the truck and the local vehicle is the sum of the distances they each covered, which equals $24$ miles. Therefore, the equation relating $a$ and $b$ is: $\newline$ rac{1}{2}a + rac{1}{6}b = 24
Simplify Total Distance Equation: To find the correct answer from the given options, we need to simplify the equation $(\frac{1}{2})a + (\frac{1}{6})b = 24$ . Multiplying both sides of the equation by $6$ to clear the fractions, we get: $\newline$ $6*(\frac{1}{2})a + 6*(\frac{1}{6})b = 6*24$ $\newline$ $3a + b = 144$ $\newline$ This equation is not in the form of any of the given options, which means we need to check our steps for any errors.