SOLUTION: Delmas flew to Detroit in 90 minutes and drove his car back home in 6 hours. If he drove 150mph slower than he flew, then how fast did he fly?

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Delmas flew to Detroit in 90 minutes and drove his car back home in 6 hours. If he drove 150mph slower than he flew, then how fast did he fly?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 215864: Delmas flew to Detroit in 90 minutes and drove his car back home in 6 hours. If he drove 150mph slower than he flew, then how fast did he fly?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Delmas flew to Detroit in 90 minutes and drove his car back home in 6 hours. If he drove 150mph slower than he flew, then how fast did he fly?

Step 1. Let x be the speed of the plane.

Step 2. Let x-150 be the speed of the car.

Step 3. Let 1.5x be the distance flew by plane where 90 minutes=1.5 hours and 60 minutes = 1 hour.

Step 4. Let 6(x-150) be the distance drove by car.

Step 5. Distances traveled by plane and car means setting equations in Steps 3 and 4 to be equal.

1.5x=6%28x-150%29

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


YOUR ANSWER


  • This is an equation! Solutions: x=200.
  • Graphical form: Equation 1.5x=6%2A%28x-150%29 was fully solved.
  • Text form: 1.5x=6*(x-150) simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+1.5x=6%2A%28x-150%29+%29
    For tutors: simplify_cartoon( 1.5x=6*(x-150) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 1.5%2Ax=highlight_red%28+6%2A%28x-150%29+%29.
Moved these terms to the left highlight_green%28+-6%2A%28x-150%29+%29
It becomes 1.5%2Ax-highlight_green%28+6%2A%28x-150%29+%29=0.
Look at 1.5%2Ax-highlight_red%28+6%2A%28x-150%29+%29=0.
Expanded term -6 by using associative property on %28x-150%29
It becomes 1.5%2Ax-highlight_green%28+6%2Ax+%29%2Bhighlight_green%28+6%2A150+%29=0.
Look at 1.5%2Ax-6%2Ax%2Bhighlight_red%28+6+%29%2Ahighlight_red%28+150+%29=0.
Multiplied numerator integers
It becomes 1.5%2Ax-6%2Ax%2Bhighlight_green%28+900+%29=0.
Look at highlight_red%28+1.5%2Ax+%29-highlight_red%28+6%2Ax+%29%2B900=0.
Eliminated similar terms highlight_red%28+1.5%2Ax+%29,highlight_red%28+-6%2Ax+%29 replacing them with highlight_green%28+%281.5-6%29%2Ax+%29
It becomes highlight_green%28+%281.5-6%29%2Ax+%29%2B900=0.
Look at %28highlight_red%28+1.5+%29-highlight_red%28+6+%29%29%2Ax%2B900=0.
Added fractions or integers together
It becomes %28-highlight_green%28+45%2F10+%29%29%2Ax%2B900=0.
Look at highlight_red%28+%28-highlight_red%28+45%2F10+%29%29%2Ax+%29%2B900=0.
Remove unneeded parentheses around factor highlight_red%28+45+%29,highlight_red%28+1%2F10+%29
It becomes -highlight_green%28+45+%29%2Fhighlight_green%28+10+%29%2Ax%2B900=0.
Look at -highlight_red%28+45+%29%2Fhighlight_red%28+10+%29%2Ax%2B900=0.
Factors 45 and 10 have greatest common factor (GCF) of 5. Reducing fraction.
It becomes -highlight_green%28+9+%29%2Fhighlight_green%28+2+%29%2Ax%2B900=0.
Look at highlight_red%28+-9%2F2%2Ax%2B900+%29=0.
Solved linear equation highlight_red%28+-9%2F2%2Ax%2B900=0+%29 equivalent to -4.5*x+900 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=200.

Universal Simplifier and Solver


Done!


With x=200, then x-150=50.

Check if distances are equal... 1.5*200=6*50 or 300=300 a true statement

Step 6. The speed of the plane is 200 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