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Two cars were moving in a straight line in opposite directions.
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Given that the distance between them was 17 kilometers, the speed of one of the cars was 45 kilometers per hour, and the cars would meet after five minutes, determine the speed of the other car.
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Okay, so here we have these two cars which are both in motion and they’re moving towards one another.
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At this particular instant in time, the cars are 17 kilometers apart.
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Also, the speed of one of the cars, we’ll just say the one on the left, is 45 kilometers per hour.
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And we’re told that if the cars were to continue moving towards one another at this rate, they would meet after a time of five minutes had elapsed.
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Knowing this, we want to determine the speed of the other car involved.
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We’ll call that speed 𝑠.
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Regarding this situation, we can say that if we add together the speeds of our two cars, then that will give us a total combined speed that covers a distance of 17 kilometers in a time of five minutes.
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In general, for any object moving at a constant speed 𝑠, that speed is equal to the distance the object travels divided by the time it takes to travel that distance.
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So when we add together 45 and 𝑠, we’ll get a combined speed that covers a distance of 17 kilometers in five minutes.
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If we subtract 45 from both sides, we get an equation where 𝑠 is the subject.
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To compute 𝑠, let’s recall that the units of 45 are kilometers per hour.
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Note that that’s different from these units of kilometers per minute.
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To put the units on the same footing, let’s recall that there’re 60 minutes in one hour.
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This means we can replace our time of one minute with one sixtieth of an hour.
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When we multiply one over 60 by five, we get one over 12.
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And then if we multiply both numerator and denominator of this fraction by 12, we get 12 times 17 kilometers per hour.
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𝑠 then equals 12 times 17 minus 45, or 159 kilometers per hour.
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This is the speed of the second car involved so that combined these cars cover 17 kilometers in a time of five minutes.