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

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) (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.
.
Check for lowest common denominator carefully. LCD is .
Multiply left and right members by .
.
.

---
65=5*13;
60=2*2*3*5;
LCD is 2*2*3*5*13=780
Answer by richwmiller(17219) (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

RELATED QUESTIONS
Tom drove at a speed of 45 mph for t hours. How far did tom... (answered by Alan3354)
Your mom and dad took turns driving on a 580 mile road trip that took 10 hours to... (answered by KMST)
Your brother and sister took turns driving on a 580 mile trip that took 10 hours to... (answered by mananth)
Yvette and Juan took turns driving on a 580 mile trip that took 10 hours to complete.... (answered by stanbon)
Ann left the store and drove toward the lake at an average speed of 70 km/h. Some time... (answered by solver91311)
Your aunt and uncle took turns driving on a 580-mile trip that took 10 hours. Your uncle (answered by josgarithmetic,MathTherapy)
Tom drove from Toronto to Owen sound, a distance of 550km. The trip took 7 hours. Tom... (answered by josgarithmetic)
Grace drove a distance of 189 miles. Part of the time she averaged 65mph and for the... (answered by macston)
Hi.Thanks for responding and helping me solve this problem.Please show the work. 1.For... (answered by ankor@dixie-net.com)