During rush houradriana can drive 30 miles using the side ro

During rush hour,adriana can drive 30 miles using the side roads in the same time that it takes to travel 15 miles on the Freeway. If Adriana\'a rate on the side roads is 6 mi/hr faster than her rate on the freeway, find her rate on the side roads.
6,8,12,14
Is the correct answer 6?

Solution

Is the correct answer 6?I THINK THAT 6 IS HER RATE ON THE FREEWAY????

Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let r=Adriana\'s rate on the freeway
then r+6=her rate on the side roads
time on the side roads=30/(r+6)
time on the freeway=15/r
and we are told that the above two times are equal, so:
30/(r+6)=15/r multiply each side by r(r+6) {or cross-multiply}
30r=15(r+6) get rid of parens
30r=15r+90 subtract 15 from both sides
30r-15r=15r-15r+90 collect like terms
15r=90 divide both sides by 15
r=6 mph--------------------------------her rate on the freeway
r+6=6+6=12mph----------------------------her rate on the side roads
CK
30/12=15/6
15/6=15/6
Hope this helps