Cities A and B are 45 miles apart. Alicia lives in A and Beth lives in B. Alicia bikes towards B at

Question

Cities A and B are 45 miles apart. Alicia lives in A and Beth lives in B. Alicia bikes towards B at 18 miles per hour. Leaving at the same time, Beth bikes toward A at 12 miles per hour. How many miles from City A will they be when they meet?

Accepted Answer

{"content":[{"content":[{"marks":[{"type":"bold"}],"text":"Step 1 (Find Relative Speed):","type":"text"},{"text":" Alicia and Beth are traveling towards each other from cities ","type":"text"},{"attrs":{"latex":"A"},"type":"math_inline"},{"type":"text","text":" and "},{"attrs":{"latex":"B"},"type":"math_inline"},{"type":"text","text":", which are 45 miles apart. Since they are moving towards each other, their relative speed of approach is the sum of their individual speeds:"}],"type":"paragraph"},{"type":"math_block","attrs":{"latex":"\text{Relative Speed} = 18 \text{ mph} + 12 \text{ mph} = 30 \text{ mph}"}},{"content":[{"marks":[{"type":"bold"}],"text":"Step 2 (Calculate Time to Meet):","type":"text"},{"text":" The time ","type":"text"},{"attrs":{"latex":"t"},"type":"math_inline"},{"text":" in hours it takes for them to meet is:","type":"text"}],"type":"paragraph"},{"type":"math_block","attrs":{"latex":"t = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{45 \text{ miles}}{30 \text{ mph}} = 1.5 \text{ hours}"}},{"content":[{"marks":[{"type":"bold"}],"text":"Step 3 (Find Distance from City A):","type":"text"},{"type":"text","text":" Alicia started from City "},{"attrs":{"latex":"A"},"type":"math_inline"},{"type":"text","text":" and traveled for "},{"attrs":{"latex":"1.5"},"type":"math_inline"},{"text":" hours at a speed of ","type":"text"},{"attrs":{"latex":"18"},"type":"math_inline"},{"type":"text","text":" mph. Her distance from City "},{"type":"math_inline","attrs":{"latex":"A"}},{"text":" when they meet is:","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"\text{Distance} = \text{Speed} \times \text{Time} = 18 \text{ mph} \times 1.5 \text{ hours} = 27 \text{ miles}"},"type":"math_block"},{"type":"paragraph","content":[{"marks":[{"type":"bold"}],"text":"Step 4 (Conclusion):","type":"text"},{"text":" They will be exactly ","type":"text"},{"marks":[{"type":"code"}],"text":"27","type":"text"},{"text":" miles from City A when they meet.","type":"text"}]}],"type":"doc"}

Guide / Hint

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