Lesson Unusual catching-up problem
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<H2>Unusual catching-up problem</H2> <H3>Problem 1</H3>Jim and John drive from point A to point B in separate cars. Jim leaves at 6 am and arrives at 4 pm. John leaves at 10 am and arrives at 3 pm. Assume both men drive at constant speeds. Find when John catches up with Jim. <B>Solution</B> <pre> Jim covered the distance from A to B in 10 hours, according to the condition. John covered the same distance in 5 hours, according to the condition. Hence, John' speed is two times Jim' speed. OK. Let u be the Jim' speed. Then John' speed is (2u). Let's write the equation/equations of theirs movements. Let "t" be the time counted from Jim' start at 6:00 am. Then Jim's distance from A at the time moment t is x = u*t, while John's distance from A at the time t is y = (2u)*(t-4). At the catching moment x = y, or ut = (2u)*(t-4), ut = 2ut - 8u ====> ut = 8u ====> t = 8. So, John will catch up Jim 8 hours after 6:00 am, i.e. at 2:00 pm. <U>Answer</U>. 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