SOLUTION: Bob leaves at 9am heading due north at 9mph. Tom leaves at 9:30am heading due south at 4mph. At what time will Bob and Tom be 10 miles apart?

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Bob leaves at 9am heading due north at 9mph. Tom leaves at 9:30am heading due south at 4mph. At what time will Bob and Tom be 10 miles apart?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 213418: Bob leaves at 9am heading due north at 9mph. Tom leaves at 9:30am heading due south at 4mph. At what time will Bob and Tom be 10 miles apart?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Bob leaves at 9am heading due north at 9mph. Tom leaves at 9:30am heading due south at 4mph. At what time will Bob and Tom be 10 miles apart?

Step 1. Bob traveled for one-half hour before Tom leaves at 9:30 am. Let this distance be d0=9*0.5=4.5 miles.

Step 2. So Total Distance traveled by Bob dBob=4.5+9t where t is the amount of time at which Bob and Tom are 10 miles apart.

Step 3. Total Distance traveled by Tom is dTom = 4*t.

Step 4. But dBob+dTom = 10 miles

Step 5. So substitute equation in Steps 2 and 3 into Step 4.

4.5%2B9t%2B4%2At=10 Solving this equation will yield the following steps:

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


YOUR ANSWER


  • This is an equation! Solutions: t=0.423076923076923.
  • Graphical form: Equation 4.5%2B9t%2B4%2At=10 was fully solved.
  • Text form: 4.5+9t+4*t=10 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+4.5%2B9t%2B4%2At=10+%29
    For tutors: simplify_cartoon( 4.5+9t+4*t=10 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+4.5+%29%2B9%2At%2B4%2At=10.
Moved 4.5 to the right of expression
It becomes 9%2At%2B4%2At%2Bhighlight_green%28+4.5+%29=10.
Look at highlight_red%28+9%2At+%29%2Bhighlight_red%28+4%2At+%29%2B4.5=10.
Eliminated similar terms highlight_red%28+9%2At+%29,highlight_red%28+4%2At+%29 replacing them with highlight_green%28+%289%2B4%29%2At+%29
It becomes highlight_green%28+%289%2B4%29%2At+%29%2B4.5=10.
Look at %28highlight_red%28+9+%29%2Bhighlight_red%28+4+%29%29%2At%2B4.5=10.
Added fractions or integers together
It becomes %28highlight_green%28+13+%29%29%2At%2B4.5=10.
Look at highlight_red%28+%28highlight_red%28+13+%29%29%2At+%29%2B4.5=10.
Remove unneeded parentheses around factor highlight_red%28+13+%29
It becomes highlight_green%28+13+%29%2At%2B4.5=10.
Look at 13%2At%2B4.5=highlight_red%28+10+%29.
Moved these terms to the left highlight_green%28+-10+%29
It becomes 13%2At%2B4.5-highlight_green%28+10+%29=0.
Look at 13%2At%2Bhighlight_red%28+4.5+%29-highlight_red%28+10+%29=0.
Added fractions or integers together
It becomes 13%2At-highlight_green%28+55%2F10+%29=0.
Look at 13%2At-highlight_red%28+55+%29%2Fhighlight_red%28+10+%29=0.
Factors 55 and 10 have greatest common factor (GCF) of 5. Reducing fraction.
It becomes 13%2At-highlight_green%28+11+%29%2Fhighlight_green%28+2+%29=0.
Look at highlight_red%28+13%2At-11%2F2+%29=0.
Solved linear equation highlight_red%28+13%2At-11%2F2=0+%29 equivalent to 13*t-5.5 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: t=0.423076923076923.

Universal Simplifier and Solver


Done!



Step 6. t=0.42307 hours or t = 0.42307*60 minutes/hour = 25.42 minutes.

Step 7. Time is therefore 9:30 am plus 25.42 minutes or 9:55 am.


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