SOLUTION: A race car traveling at full speed takes 8 minutes longer to travel 50 miles than to travel 30 miles. What is the race car's full speed?

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Question 166370: A race car traveling at full speed takes 8 minutes longer to travel 50 miles than to travel 30 miles. What is the race car's full speed?
Answer by MRperkins(300) About Me  (Show Source):
You can put this solution on YOUR website!
miles per hour(speed)=distance/time
m%2Fh=d%2Ft
equation 1 m%2Fh=%2830miles%29%2F%28%28t%29hours%29
equation 2 m%2Fh=%2850miles%29%2F%28%28t%29hours%2B8%28minutes%29%29
set the equations = to each other
%2830miles%29%2F%28%28t%29hours%29=%2850miles%29%2F%28%28t%29hours%2B8%28minutes%29%29
convert the 8 minutes to hours. 8(minutes)=8/60 hours which reduces to 2/15 hours.
so now you have the equation:
%2830miles%29%2F%28%28t%29hours%29=%2850miles%29%2F%28%28t%2B2%2F15%29hours%29
Solve for t:
cross multiply and get
30%28t%2B2%2F15%29=50%28t%29
30t%2B60%2F15=50t
subtract 30t from each side
60/15=20t
multiply each side by 15
60=300t
divide each side by 300
1%2F5=t
.
we remember that t=time in hours and we are trying to find speed. so we plug t into either speed formula to find our speed.
First formula: equation 1 m%2Fh=%2830miles%29%2F%28%281%2F5%29hours%29
Second formula: equation 2 m%2Fh=%2850miles%29%2F%28%281%2F5%29hours%2B%282%2F15%29%28hours%29%29
.
Answer: Top speed is 150miles/hour
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