SOLUTION: Ann and Tom took turns driving for a total of 10 hours. On average, Ann drove at 65mph and tom at 60mph. For how long did each drive, and how far, if Ann drove 100 miles farther th

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Question 896545: Ann and Tom took turns driving for a total of 10 hours. On average, Ann drove at 65mph and tom at 60mph. For how long did each drive, and how far, if Ann drove 100 miles farther than Tom?
Found 2 solutions by josgarithmetic, richwmiller:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The given information into a table assigning for d:
Uniform Rate Rule, RT=D equivalent to T=D/R


_____________________speed______time_________distance
Ann__________________65________(___)_________d+100
Tom__________________60________(___)__________d
TOTAL___________________________10

_____________________speed______time_________distance
Ann__________________65________(d+100)/65_________d+100
Tom__________________60________(d/60)__________d
TOTAL___________________________10


Question is for TIMES that each drove, but this requires first solving for d.
highlight%28%28d%2B100%29%2F65%2Bd%2F60=10%29.
Check for lowest common denominator carefully. LCD is 5%2A12%2A13=780.
Multiply left and right members by 5%2A12%2A13.
.
.



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65=5*13;
60=2*2*3*5;
LCD is 2*2*3*5*13=780

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
65a+60t=d,
a+t=10,
65a=60t+100
a = 28/5=, t = 22/5, d = 628
5.6 hours for Ann
4.4 hours for Tom
check
28/5+22/5=50/5=10
65*28/5=364
60*22/5=264
364+264=628
ok