SOLUTION: 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 increas

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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.
Found 2 solutions by drj, Stitch:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
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%2A%281hour%2F%2860+minutes%29%29+=%283%2F4%29hour=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%2B299-52t=317

6t%2B299=317

Subtract 299 from both sides of the equation

6t%2B299-299=317-299

6t=18

Divide by 6 to both sides of the equation

6t%2F6=18%2F6

t=3 and 5.75-3=2.75

Check distance traveled if equal to 317

58%2A3%2B52%2A2.75=317

174%2B143=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.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV

Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Given: Miles Total (Mt) = 317mi, Time = 5h - 45min
Our first equation: 317mi = {X*58mi/h} + {Y*52mi/h}
I converted the minutes to hours:
5h 45min = 5.75h ((45m/(60m/h))=.75
Our second equation: 5.75h = X + Y
Solve the 2nd equation for X:
5.75 = X + Y (Subtract Y from both sides)
5.75 - Y = X
Substitute 5.75h - Y in for X in Equation 1:
317mi = {{5.75h - Y} * 58mi/h} + {Y * 52mi/h}
317mi = {5.75h * 58mi/h} - {Y * 58mi/h} + {Y * 52mi/h} Then simplify
317mi = 333.5mi - Y*6mi/h Then add Y*6mi/h and -317mi to both sides
Y*6mi/h = 333.5mi - 317mi
Y*6mi/h = 16.5mi Then divide both sides by 6mi/h
Y = 2.75h
Plug 2.75h in for Y in the second equation:
5.75h = X + Y
5.75h = X + 2.75 Subtract 2.75 from both sides
3h = X