Commuting Students

[kelly1]

Another word problem! Thanks for any help.

1/4 of the undergraduate students commute, 1/3 of graduate students commute. 1/10 of the undergraduate students drive more than 40 miles daily and 1/6 of the graduate students drive more than 40 miles daily. If there are twice as many undergraduate students as there are graduate students, then what fraction of the commuters drive more than 40 miles per day?

 

[skeeter]

let U = number of undergrads
G = number of grads
C = number of commuters
D = number of commuters who drive more than 40 miles

o.k. ...

C = U/4 + G/3

D = U/10 + G/6

also know that there are twice as many undergraduate students as there are graduate students, or as an equation ... U = 2G

so, let's substitute 2G for U in the equations above ...

C = 2G/4 + G/3 = G/2 + G/3 = 5G/6

D = 2G/10 + G/6 = G/5 + G/6 = 11G/30

what we want to know is D/C, the fraction of commuters who drive over 40 miles a day ...

D/C = (11G/30)/(5G/6)

simplify the quotient of fractions above to answer the question.