Question 230585
On the first part of a 317 mile trip, a sales person averaged 58 miles per hour. The sales person averaged only 52 miles per hour on the last part of the trip because of an increased volume of traffic. The total time of the trip was 5 hours and 45 minutes. Find the amount of time at each of the two speeds.


Step 1.  distance = speed * time


Step 2.  Let t be the time traveled in the first part of the trip


Step 3.  Let 5.75-t be the time traveled in the second part of the trip since 5 hours and 45 minutes is equal to 5.75 and that {{{45 minutes*(1hour/(60 minutes)) =(3/4)hour=0.75hour}}}.


Step 4.  Let 58t be the distance traveled at 58 miles per hour.


Step 5.  Let 52(5.750-t) be the distance traveled at 52 miles per hour.


Step 6.  Then 58t+52(5.75-t)=317 since the total distance of the trip is 317 miles.


Step 7.  Solving 58t+52(5.75-t)=317 leads to the following steps


{{{58t+299-52t=317}}}


{{{6t+299=317}}}


Subtract 299 from both sides of the equation


{{{6t+299-299=317-299}}}


{{{6t=18}}}


Divide by 6 to both sides of the equation


{{{6t/6=18/6}}}


{{{t=3}}} and {{{5.75-3=2.75}}}


Check distance traveled if equal to 317


{{{58*3+52*2.75=317}}}


{{{174+143=317}}}


{{{317=317}}} which is a true statement


Step 8.  ANSWER:  The sales person traveled for 3 hours at 58 miles per hour and for 2 hours and 45 minutes (=2.75 hours) at 52 miles per hour.


I hope the above steps were helpful.


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Respectfully,
Dr J

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