SOLUTION: two buses leave the same city at the same time moving in opposite directions. One travels at a rate of 5 miles per hour faster then the other bus. After 3 hours they are 375 miles

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Question 214139: two buses leave the same city at the same time moving in opposite directions. One travels at a rate of 5 miles per hour faster then the other bus. After 3 hours they are 375 miles apart. How far did each bus travel

I think the equation I should use is D= RT but I dont get this question because I dont know the speed of both cars.
Found 2 solutions by drj, thinkingeye:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Two buses leave the same city at the same time moving in opposite directions. One travels at a rate of 5 miles per hour faster then the other bus. After 3 hours they are 375 miles apart. How far did each bus travel.

Step 1. Let x be the speed of one bus and let x+5 be the speed of the other bus.

Step 2. Distance = speed * time

Step 3. Distance of one bus = 3x and Distance of other bus = 3(x+5).

Step 4. Total Distance = Distance of one bus + Distance of other bus = 375 miles

Step 5. Combine steps 2 and 3 to get 3x+3(x+5)=375 or 6x+15=375. Solving for x yields the following steps.

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=60.
  • Graphical form: Equation 6x%2B15=375 was fully solved.
  • Text form: 6x+15=375 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+6x%2B15=375+%29
    For tutors: simplify_cartoon( 6x+15=375 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 6%2Ax%2B15=highlight_red%28+375+%29.
Moved these terms to the left highlight_green%28+-375+%29
It becomes 6%2Ax%2B15-highlight_green%28+375+%29=0.
Look at 6%2Ax%2Bhighlight_red%28+15+%29-highlight_red%28+375+%29=0.
Added fractions or integers together
It becomes 6%2Ax%2Bhighlight_green%28+-360+%29=0.
Look at 6%2Ax%2Bhighlight_red%28+-360+%29=0.
Removed extra sign in front of -360
It becomes 6%2Ax-highlight_green%28+360+%29=0.
Look at highlight_red%28+6%2Ax-360+%29=0.
Solved linear equation highlight_red%28+6%2Ax-360=0+%29 equivalent to 6*x-360 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=60.

Universal Simplifier and Solver


Done!



Step 6. Based on the above results when x=60, then distance traveled by one bus is 3x=180 miles and the other bus traveled 3(x+5)=195 miles. Adding the two distances yield that they are 375 miles part.

Step 7. ANSWER: One bus traveled 180 miles and the other traveled 195 miles.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

Answer by thinkingeye(11) About Me  (Show Source):
You can put this solution on YOUR website!
185 and 190 miles