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Salem and Vernonville and 128 miles apart. A car leaves Salem traveling towards Vernonville, and another car leaves vernonville at the same time, traveling towards Salem. The car leaving Salem averages 10 miles per hour more than the other, and they meet after 1 hour and 36 minutes. What are the average speeds of the cars? salem average, vernonville average
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Hi Mishonta;
distance=128 miles
from Vernonville...x miles/hour
from Salem...(x+10) miles/hour
time...1 hour, 36 minutes
All units of time must be in hours, not minutes.
(36 minutes)[(1 hour)/(60 minutes)]
The unit of minutes is in the numerator and denominator.  It cancels...
(36 minutes)[(1 hour)/(60 minutes)]
The only unit remaining is hour, which is what we want...
36/60 hours
3/5 hours=0.6 hours
time....1.6 hours
128 miles={(x miles/hour)+[(x+10)miles/hour]} (1.6 hours)
128 miles=[(2x+10)miles/hour](1.6 hours)
The unit of hours is in the denominator and numerator of the right side.  It cancels...
128 miles=[(2x+10)miles/hour](1.6 hours)
128 miles=[(2x+10)miles)(1.6)
The unit of miles is in the numerators of both sides of the equation.  It cancels...
128 miles=[(2x+10)miles)(1.6)
128=(2x+10)(1.6)
128=3.2x+16
Let's subtract 16 from both sides...
128-16=3.2x+16-16
112=3.2x
Let's divide both sides by 3.2
112/3.2=(3.2x)/3.2
35=x
 
from Vernonville....35 miles/hour
from Salem....(35+10) miles/hour=45 miles/hour
 

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