Lesson Selected Travel and Distance problems from the archive
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<H2>Selected Travel and Distance problems from the archive</H2> This lesson is a collection of selected Travel and Distance problems from the archive of this site. <H3>Problem 1</H3>A train leaves Orlando at 1:00 PM. A second train leaves the same city in the same direction at 3:00 PM. The second train travels 12 mph faster than the first. If the second train overtakes the first at 10:00 PM, what is the speed of each of the two trains? <A HREF=https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.1025053.html>https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.1025053.html</A> <B>Solution</B> <pre> Let u = first train' speed, in mph. Then the second train' speed is u+12 mph, according to the condition. The first train traveled 9 hours before the second train overtakes the first one. During this time the first train covered the distance of 9*u miles. The second train traveled 7 hours before overtakes the first one. During this time the second train covered the distance of 7*(u+12) miles. These distances are the same. It gives you an equation 9u = 7*(u+12), or 9u = 7u + 84 ---> 2u = 84 ---> u = {{{84/2}}} = 42 mph. Then u+12 = 54 mph. The problem is solved. <U>Answer</U>. The first train' speed is 42 mph. The second train' speed is 54 mph. </pre> <H3>Problem 2</H3>It took Andy 9 hours to drive to a rock concert. On the way home, he was able to increase his average speed by 14 mph and make the return drive in only 7 hours. What is his average speed for the drive home? <A HREF=https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.1025164.html>https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.1025164.html</A> <B>Solution</B> <pre> Your guiding equation is 9*u = 7*(u+14), where u is Andy' speed on the way to the rock concert, in mph. Each side of this equation is the distance between home and concert. Simplify and solve it: 9u = 7u + 98, 2u = 98, u = {{{98/2}}}. The solution is u = 49 mph. It is Andy' speed on the way to concert. So, the Andy' speed on the way home is 49+14 = 63 mph. </pre> <H3>Problem 3</H3>Darren drives to school in rush hour traffic and averages 32 mph. He returns home in mid-afternoon when there is less traffic and averages 48 mph. What is the distance between his home and school if the total traveling time is 1 hr 15 min? <A HREF=https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.1044747.html>https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.1044747.html</A> <B>Solution</B> <pre> Let D be the distance under the question. Then your equation is {{{D/32 + D /48}}} = {{{1}}}{{{1/4}}}. The first addend in the left side is the time of driving at 32 mph. The second addend in the left side is the time of driving at 48 mph. The right side is the total traveling time, according to the condition. To solve the equation, multiply both sides by 96, which is LCM of the denominators. You will get 3D + 2D = 120, 5D = 120, D = {{{120/5}}} = 24. <U>Answer</U>. The distance under the question is 24 miles. </pre> <H3>Problem 4</H3>Driving from point A to point B at 33 km/h takes 2 hours less than cycling at 11 km/h. How far is it from A to B? <A HREF=https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.1044716.html>https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.1044716.html</A> <B>Solution</B> <pre> Let D be the distance under the question. Then your equation is {{{D/11}}} - {{{D/33}}} = 2. (1) The first term in the left side is the time cycling at 11 km/h. The second term in the left is is the time driving at 33 km/h. The number "2" on the right is the time difference, according to the condition. To solve (1), multiply both sides by 33. You will get 3D - D = 2*33, or 2D = 66, or D = 33. <U>Answer</U>. The distance is 33 km. </pre> <H3>Problem 5</H3>A ship made a trip of 231 mi in 14 h. The ship traveled the first 98 mi at a constant rate before increasing its speed by 5 mph. It traveled another 133 mi at the increased speed. Find the rate of the ship for the first 98 mi. <A HREF=https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.1040814.html>https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.1040814.html</A> <B>Solution</B> <pre> Your equation is {{{98/u + 133/(u+5)}}} = {{{14}}}. The first addend in the left side is the time spent to cover 98 miles. The second addend is the time spent to cover 133 miles. Here "u" is he ship's rate for the first 98 mi, which is under the question. To solve it, multiply both sides by u*(u+5). You will get this quadratic equation: 98*(u+5) + 133u = 14u*(u+5). Simplify and solve it for "u": {{{14u^2 + 70u - 98u - 133u - 490}}} = {{{0}}}, or {{{14u^2 - 161u - 490}}} = {{{0}}}, {{{x[1,2]}}} = {{{(161 +- sqrt(161^2+ 4*14*490))/28}}} = {{{(161 +- sqrt(53361))/28}}} = {{{(161 +- 231)/28}}}. Only the positive root u = 14 makes sense. <U>Answer</U>. The speed under the question is 14 miles per hour. </pre> <H3>Problem 6</H3>A train travels the distance between the station A and B in 45 minutes. If the train reduces its speed by 5 km per hour it takes 48 minutes to cover this distance, what is the distance between the two stations? <A HREF=https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.1044434.html>https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.1044434.html</A> <B>Solution</B> <pre> 45 minutes = {{{3/4}}} of an hour. 48 minutes = {{{4/5}}} of an hour. Let "u" be the speed of the train in the first scenario. in {{{km/h}}}. Then the speed in the second scenario is (u-5) {{{km/h}}}. Then you have this equation {{{(4/5)*(u-5)}}} = {{{(3/4)*u}}}, which says that the distance is the same. Simplify it: {{{(4/5)*u - 4}}} = {{{(3/4)*u}}}, {{{(4/5 - 3/4)*u}}} = 4, {{{(16/20 - 15/20)*u}}} = 4, {{{(1/20)*u}}} = 4, u = 80. Thus the train speed is 80 km/h. Hence, the distance is {{{(3/4)*80}}} = 60 km. <U>Answer</U>. The distance is 60 km. </pre> My other lessons on <B>Travel and Distance</B> problems in this site are <TABLE> <TR> <TD> - <A HREF=http://www.algebra.com/algebra/homework/word/travel/Travel-and-Distance-problems.lesson>Travel and Distance problems</A> - <A HREF=https://www.algebra.com/algebra/homework/word/travel/Travel-and-Distance-problems-for-two-bodies-moving-toward-each-other.lesson>Travel and Distance problems for two bodies moving in opposite directions</A> - <A HREF=https://www.algebra.com/algebra/homework/word/travel/Typical-catching-up-Travel-and-Distance-problems.lesson>Travel and Distance problems for two bodies moving in the same direction (catching up)</A> - <A HREF=http://www.algebra.com/algebra/homework/NumericFractions/Using-fractions-to-solve-Travel-problems.lesson>Using fractions to solve Travel problems</A> - <A HREF=http://www.algebra.com/algebra/homework/word/travel/Wind-and-Current-problems.lesson>Wind and Current problems</A> - <A HREF=http://www.algebra.com/algebra/homework/word/travel/More-problems-on-upstream-and-downstream-round-trips.lesson>More problems on upstream and downstream round trips</A> - <A HREF=http://www.algebra.com/algebra/homework/word/travel/Wind-and-Current-problems-solvable-by-quadratic-equations.lesson>Wind and Current problems solvable by quadratic equations</A> - <A HREF=https://www.algebra.com/algebra/homework/word/travel/Unpowered-raft-moving-downstream-along-a-river.lesson>Unpowered raft floating downstream along a river</A> - <A HREF=https://www.algebra.com/algebra/homework/word/travel/Selected-problems-from-the-archive-on-a-boat-floating-Upstream-and-Downstream.lesson>Selected problems from the archive on the boat floating Upstream and Downstream</A> - <A HREF=https://www.algebra.com/algebra/homework/word/travel/Selected-problems-from-the-archive-on-a-plane-flying-with-and-against-the-wind.lesson>Selected problems from the archive on a plane flying with and against the wind</A> - <A HREF=https://www.algebra.com/algebra/homework/word/travel/Had-a-car-move-faster-it-would-arrive-quicker.lesson>Had a car move faster it would arrive sooner</A> - <A HREF=http://www.algebra.com/algebra/homework/word/travel/How-far-do-you-live-from-school.lesson>How far do you live from school?</A> - <A HREF=http://www.algebra.com/algebra/homework/word/travel/One-unusual-Travel-problem.lesson>One unusual Travel problem</A> - <A HREF=http://www.algebra.com/algebra/homework/word/travel/Another-unusual-Travel-problem.lesson>Another unusual Travel problem (Arnold's problem on two walking old women)</A> - <A HREF=http://www.algebra.com/algebra/homework/word/travel/Travel-problem-on-a-messenger-moving-back-and-forth-along-the-marching-army-column.lesson>Travel problem on a messenger moving back and forth along the marching army's column</A> - <A HREF=https://www.algebra.com/algebra/homework/word/travel/A-person-walking-along-the-street-and-the-buses-traveling-in-the-same-and-opposite-directions.lesson>A person walking along the street and buses traveling in the same and opposite directions</A> </TD> <TD> - <A HREF=http://www.algebra.com/algebra/homework/word/travel/Calculating-an-average-speed.lesson>Calculating an average speed: a train going from A to B and back</A> - <A HREF=http://www.algebra.com/algebra/homework/word/travel/One-more-problem-on-calculating-an-average-speed.lesson>One more problem on calculating an average speed</A> - <A HREF=http://www.algebra.com/algebra/homework/word/travel/Clock-problems.lesson>Clock problems</A> - <A HREF=https://www.algebra.com/algebra/homework/word/travel/Advanced-clock-problems.lesson>Advanced clock problems</A> - <A HREF=http://www.algebra.com/algebra/homework/word/travel/Problems-on-bodies-moving-on-a-circle.lesson>Problems on bodies moving on a circle</A> - <A HREF=http://www.algebra.com/algebra/homework/word/travel/A-train-passing-a-telegraph-post-and-passing-a-bridge.lesson>A train passing a telegraph post and passing a bridge</A> - <A HREF=http://www.algebra.com/algebra/homework/word/travel/A-train-passing-a-platform.lesson>A train passing a platform</A> - <A HREF=http://www.algebra.com/algebra/homework/word/travel/A-train-passing-a-tunnel.lesson>A train passing through a tunnel</A> - <A HREF=http://www.algebra.com/algebra/homework/word/travel/A-light-rail-train-passing-a-walking-person.lesson>A light-rail train passing a walking person</A> - <A HREF=http://www.algebra.com/algebra/homework/word/travel/A-train-passing-another-train.lesson>A train passing another train</A> - <A HREF=https://www.algebra.com/algebra/homework/word/travel/A-man-crossing-a-bridge-when-a-train-comes-from-behind.lesson>A man crossing a bridge and a train coming from behind</A> - <A HREF=https://www.algebra.com/algebra/homework/word/travel/27-A-problem-on-a-rower-going-on-a-river-who-missed-the-bottle-of-whiskey-under-a-bridge.lesson>A rower going on a river who missed the bottle of whiskey under a bridge</A> - <A HREF=https://www.algebra.com/algebra/homework/word/travel/Non-traditional-Travel-and-Distance-problems.lesson>Non-traditional Travel and Distance problems</A> - <A HREF=https://www.algebra.com/algebra/homework/word/travel/The-distance-covered-by-a-free-falling-body-during-last-second-of-the-fall.lesson>The distance covered by a free falling body during last second of the fall</A> - <A HREF=https://www.algebra.com/algebra/homework/word/travel/The-Doppler-shift.lesson>The Doppler Shift</A> - <A HREF=https://www.algebra.com/algebra/homework/word/travel/Entertainment-Travel-and-Distance-problems.lesson>Entertainment Travel and Distance problems</A> - <A HREF=https://www.algebra.com/algebra/homework/word/travel/OVERVIEW-of-lessons-on-Travel-and-Distance.lesson>OVERVIEW of lessons on Travel and Distance</A> </TD> </TR> </TABLE> Use this file/link <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A> to navigate over all topics and lessons of the online textbook ALGEBRA-I.
