SOLUTION: An auto averaged 40 mph for part of a trip and 50 mph for the remainder. If the 5-hour trip covered 210 miles, for how long did the car average 40mph?

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Question 215677: An auto averaged 40 mph for part of a trip and 50 mph for the remainder.
If the 5-hour trip covered 210 miles, for how long did the car average 40mph?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
An auto averaged 40 mph for part of a trip and 50 mph for the remainder.
If the 5-hour trip covered 210 miles, for how long did the car average 40mph?

Step 1. Let x be the length of time when traveling 40 mph.

Step 2. Let 5-x be the length of time traveling 50 mph.

Step 3. Let 40x be the distance traveled at 40 mph.

Step 4. Let 50(5-x) be the distance traveled at 50 mph.

Step 5. Then 40x+ 50(5-x)=210 as given by the problem statement.

The following steps will solve this equation

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


YOUR ANSWER


  • This is an equation! Solutions: x=4.
  • Graphical form: Equation 40x%2B50%2A%285-x%29=210 was fully solved.
  • Text form: 40x+50*(5-x)=210 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+40x%2B50%2A%285-x%29=210+%29
    For tutors: simplify_cartoon( 40x+50*(5-x)=210 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 40%2Ax%2B50%2A%28highlight_red%28+5+%29-x%29=210.
Moved 5 to the right of expression
It becomes 40%2Ax%2B50%2A%28-x%2Bhighlight_green%28+5+%29%29=210.
Look at 40%2Ax%2B50%2A%28-x%2B5%29=highlight_red%28+210+%29.
Moved these terms to the left highlight_green%28+-210+%29
It becomes 40%2Ax%2B50%2A%28-x%2B5%29-highlight_green%28+210+%29=0.
Look at 40%2Ax%2Bhighlight_red%28+50%2A%28-x%2B5%29+%29-210=0.
Expanded term 50 by using associative property on %28-x%2B5%29
It becomes 40%2Ax-highlight_green%28+50%2Ax+%29%2Bhighlight_green%28+50%2A5+%29-210=0.
Look at 40%2Ax-50%2Ax%2Bhighlight_red%28+50+%29%2Ahighlight_red%28+5+%29-210=0.
Multiplied numerator integers
It becomes 40%2Ax-50%2Ax%2Bhighlight_green%28+250+%29-210=0.
Look at 40%2Ax-50%2Ax%2Bhighlight_red%28+250+%29-highlight_red%28+210+%29=0.
Added fractions or integers together
It becomes 40%2Ax-50%2Ax%2Bhighlight_green%28+40+%29=0.
Look at highlight_red%28+40%2Ax+%29-highlight_red%28+50%2Ax+%29%2B40=0.
Eliminated similar terms highlight_red%28+40%2Ax+%29,highlight_red%28+-50%2Ax+%29 replacing them with highlight_green%28+%2840-50%29%2Ax+%29
It becomes highlight_green%28+%2840-50%29%2Ax+%29%2B40=0.
Look at %28highlight_red%28+40+%29-highlight_red%28+50+%29%29%2Ax%2B40=0.
Added fractions or integers together
It becomes %28highlight_green%28+-10+%29%29%2Ax%2B40=0.
Look at %28highlight_red%28+-10+%29%29%2Ax%2B40=0.
Removed extra sign in front of -10
It becomes %28-highlight_green%28+10+%29%29%2Ax%2B40=0.
Look at highlight_red%28+%28-highlight_red%28+10+%29%29%2Ax+%29%2B40=0.
Remove unneeded parentheses around factor highlight_red%28+10+%29
It becomes -highlight_green%28+10+%29%2Ax%2B40=0.
Look at highlight_red%28+-10%2Ax%2B40+%29=0.
Solved linear equation highlight_red%28+-10%2Ax%2B40=0+%29 equivalent to -10*x+40 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=4.

Universal Simplifier and Solver


Done!



With x=4, then 5-x=1.

Check distance...4*40+1*50=210...which is a true statement

Step 6. ANSWER. The car traveled for 4 hours at 40 mph.



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.

Good luck in your studies!

Respectfully,
Dr J