Question 654675
over a distance a car traveling 40 mph, 
the car then drives that same distance 10 mph, 
what is the average mph for the whole trip?
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let d = the distance traveled at 40 mph and the distance traveled at 10 mph
let a = the average mph for the trip
:
Write a time equation; time = dist/speed
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40mph time + 10mph time = total time
{{{d/40}}} + {{{d/10}}} = {{{(2d)/a}}}
multiply by 40a, to clear the denominators
40a*{{{d/40}}} + 40a*{{{d/10}}} = 40a*{{{(2d)/a}}}
Cancel the denominators
ad + 4ad = 40(2d)
5ad = 80d
divide both sides by d
5a = 80
a = 80/5
a = 16 mph is the average for the trip
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