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?


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+9t+4*t=10}}}  Solving this equation will yield the following steps:


*[invoke explain_simplification "4.5+9t+4*t=10" ]


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