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?

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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)   (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.

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 was fully solved.
  • Text form: 4.5+9t+4*t=10 simplifies to 0=0
  • Cartoon (animation) form:
    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 .
Moved 4.5 to the right of expression
It becomes .
Look at .
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 .
Look at .
Added fractions or integers together
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+13+%29
It becomes .
Look at .
Moved these terms to the left highlight_green%28+-10+%29
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Factors 55 and 10 have greatest common factor (GCF) of 5. Reducing fraction.
It becomes .
Look at .
Solved linear equation highlight_red%28+13%2At-11%2F2=0+%29 equivalent to 13*t-5.5 =0
It becomes .
Result:
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.

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Good luck in your studies!

Respectfully,
Dr J