Lesson Other basic arithmetic Travel & Distance problems
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<H2>Other basic arithmetic Travel & Distance problems</H2> <H3>Problem 1</H3>A train moves at the speed of 36 kilometers per hour. It takes for the train 12 seconds to pass a telegraph post. Find the length of the train. <B>Solution</B> <pre> The speed of 36 kilometers per hour is the same as {{{36000/3600}}} = 10 meters per second. Since the train passes a telegraph post in 12 seconds, it means that in 12 seconds the train covers the distance equal to its length. The distance is time*rate = 12 seconds * 10 meters per second = 120 meters. Hence, the length of the train is 120 meters. <U>ANSWER</U>. The length of the train is 120 meters. </pre> <H3>Problem 2</H3>A train has the length of 96 meters. It moves uniformly with a constant speed. It takes for the train 12 seconds to pass a telegraph post. Find the speed of the train. <B>Solution</B> <pre> So, every 12 seconds the train moves 96 meters forward. So, its speed is {{96/8}}} = 12 meters per second, or {{{(12*3600)/1000}}} = 43. kilometers per hour. <U>ANSWER</U>. The speed of the train is 43.2 kilometers per hour. </pre> <H3>Problem 3</H3>A train which has a length of 90 meters is traveling at a speed of 36 kilometers per hour. It passes a platform 120 meters long. How long does it take the train to pass the platform from the moment the front of the train comes up to the closest end of the platform to the moment the rear of the train comes up to the other end of the platform? <B>Solution</B> <pre> The speed of 36 kilometers per hour is the same as {{{36000/3600}}} = 10 meters per second. From the moment the front of the train comes up to the closest end of the platform to the moment the rear of the train comes up to the other end, the train moves forward 90 + 120 = 210 meters. Hence, the time for the train to pass the platform is {{{210/10}}} = 21 seconds. <U>ANSWER</U>. The time for the train to pass the platform is {{{210/10}}} = 21 seconds. </pre> <H3>Problem 4</H3>A train which has a length of 120 meters is traveling at a speed of 54 kilometers per hour. It passes a tunnel 180 meters long. How long does it take the train to pass the tunnel from the moment the front of the train comes up to the closest end of the tunnel to the moment the rear of the train comes up to the other end of the tunnel? <B>Solution</B> <pre> The speed of 54 kilometers per hour is the same as {{{54000/3600}}} = 15 meters per second. From the moment the front of the train comes up to the closest end of the tunnel to the moment the rear of the train comes up to the other end, the train moves forward 120 + 180 = 300 meters. Hence, the time for the train to pass the tunnel is {{{300/15}}} = 20 seconds. <U>ANSWER</U>. The time for the train to pass the tunnel is {{{300/15}}} = 20 seconds. </pre> <H3>Problem 5</H3>It took a train 65 seconds from starting to cross a bridge of length 1440 m to completely pass over the bridge. It also took the train 75 seconds from when it entered a 1680 m tunnel to completely pass through the tunnel. Find the speed of the train and the length of the train. <B>Solution</B> <pre> For passing the bridge, the train should move forward 1440 meters plus its own length. The train spends 65 seconds for it For passing the tunnel, the train should move forward 1680 meters plus its own length. The train spends 75 seconds for it So, the train spends 75-65 = 10 seconds to cover the distance equal the difference 1680-1440 = 240 meters. From it, we find the speed of the train as {{{240/10}}} = 24 meters per second, or {{{24*(3600/1000)}}} = 86.4 kilometers per hour. Next, in 65 seconds, the train moves forward in 65*24 = 1560 meters. Of them, 1560 - 1440 = 120 meters is the length of the train. Thus the train length is 120 meters and the train speed is 24 meters per second, or 86.4 kilometers per hour. </pre> <H3>Problem 6</H3>Two trains are approaching each other on parallel tracks. Train A is 1/5 of a mile in length. It travels east at a speed of 40 mph. Train B is 1/8 of a mile in length. It travels west at a speed of 50 mph. From the moment the trains meet(that is when their noses touch the same plane perpendicular to the tracks), how much time elapses until their tails completely pass one another. <B>Solution</B> <pre> The starting moment for our consideration is when the trains noses touch the same plane perpendicular to the tracks. At this time moment, the ending points of the trains are at the distance equal to the sum of the lengths of trains, i.e. {{{1/5+1/8}}} = {{{5/40 + 5/40}}} = {{{13/40}}} of a mile. These two ending points moves/approach toward each other with the speed, which is the sum of the speeds of the trains, i.e. 40 + 50 = 90 miles per hour. It is the relative speed approaching the ending points. The process will complete when the ending points will meet each other. The time is the initial distance between end points divided by the relative speed of approaching {{{the_initial_distance_between_end_points/the_relative_speed_of_approaching}}}= {{{((13/40))/90}}} = {{{13/3600}}} of an hour, which is 13 seconds. </pre> My other lessons on arithmetic word problems in this site are <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Arithmetic-word-problems-to-solve-them-MENTALLY.lesson>Arithmetic word problems to solve them MENTALLY</A> <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Solving-arithmetic-word-problems-by-reasoning.lesson>Solving arithmetic word problems by reasoning</A> <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Simple-arithmetic-word-problems-solved-in-a-right-way.lesson>Simple arithmetic word problems solved in a right way</A> <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Arithmetic-coin-problems.lesson>Arithmetic coin problems</A> <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Simple-arithmetic-word-problems-on-rate-of-work.lesson>Simple arithmetic word problems on "rate of work" </A> <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Simple-and-simplest-arithmetic-Travel-and-Distanse-problems.lesson>Simple and simplest arithmetic Travel & Distance problems</A> <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Typical-arithmetic-Travel-and-Distance-problems.lesson>Typical arithmetic Travel & Distance problems</A> <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Entertaining-catching-up-arithmetic-Travel-and-Distance-problems.lesson>Entertaining catching up arithmetic Travel & Distance problems</A> <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Arithmetic-word-problems-on-Travel-and-Distance.lesson>Advanced arithmetic word problems on Travel & Distance</A> <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Finding-travel-time-and-average-rate.lesson>Finding travel time and average rate</A> <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Flying-back-and-forth.lesson>Flying back and forth</A> <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/OVERVIEW-of-lessons-on-arithmetic-word-problems.lesson>OVERVIEW of the first group of lessons on arithmetic word problems</A> To see the whole list of lessons on arithmetic problems, use this link <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Arithmetic-problems-YOUR-ONLINE-TEXTBOOK.lesson>Arithmetic problems - YOUR ONLINE TEXTBOOK</A> It is your way to the entry page of the online textbook on Arithmetic problems.
