SOLUTION: Robert can drive 40 miles using the side roads in the same time that it takes to travel 30 miles on the freeway. If Robert's rate on the side road is 7 miles an hour faster than hi

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Question 103379: Robert can drive 40 miles using the side roads in the same time that it takes to travel 30 miles on the freeway. If Robert's rate on the side road is 7 miles an hour faster than his rate on the freeway, find his rate on the side road. I need help contructing the equation to solve for the rate. I am confused because there is no time given.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
let x=rate on side roads ... in the same time, he can only go 3/4 as far on the freeway, so the freeway rate is (3/4)x

(3/4)x+7=x ... 7=(1/4)x ... 28=x

using t=d/r ... the times are the same so 40/r=30/(r-7)

cross multiplying gives 40r-280=30r ... 10r=280 ... r=28