SOLUTION: Please help solve this problem. This question is from a teacher created worksheet. Two cars leave the same city. The first car is travelling at 40 mi/hr. One hour later the sec

Question 95408: Please help solve this problem. This question is from a teacher created worksheet.
Two cars leave the same city. The first car is travelling at 40 mi/hr. One hour later the second car leaves travelling at 55 mi/hr along the same road. In how many hours will the 2nd car overtake the first car?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Now we know that the 2nd car will have overtaken the first car when they have both travelled the same distance.
Let t=time travelled by the first car
then (t-1)=time travelled by the 2nd car (time to overtake)
distance(d)=rate(r) times time(t) or d=rt; t=d/r and r=d/t
Distance first car travels = 40*t
Distance 2nd car travels=55*(t-1)
When 2nd car overtakes, these distances are the same:
40*t=55(t-1) get rid of parens
40t=55t-55 subtract 55t from both sides
40t-55t=55t-55t-55 collect like terms
-15t=-55 divide both sides by -15
t=11/3 or 3.66667 hrs
t-1=3.66667-1=2.666667 hrs--------------time for 2nd car to overtake
CK
40*3.66667=55*2.66667
146.668=146.668

Hope this helps---ptaylor

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