1. The length of a rectangular floor is 1 meter less thantwice its width. If a d

Question

1. The length of a rectangular floor is 1 meter less thantwice its width. If a diagnol of the rectangle is 17 meters, findthe length and width of the floor. 2. On a 135-mile bicyclenexcursion,  Maria averaged5 miles per hour faster for the first 60 miles than she did for thelast 75 miles. The entire trip took 8 hours. Find the rate for thefirst 6 miles. 1. The length of a rectangular floor is 1 meter less thantwice its width. If a diagnol of the rectangle is 17 meters, findthe length and width of the floor. 2. On a 135-mile bicyclenexcursion,  Maria averaged5 miles per hour faster for the first 60 miles than she did for thelast 75 miles. The entire trip took 8 hours. Find the rate for thefirst 6 miles.

Explanation / Answer

1. Let w=width, then 2w-1=length.    The diagonal is the hypotenuse of the right trianglewith legs w and 2w-1. So, using the Pythagorean theorem,   w2+(2w-1)2=172=289    w2+4w2-4w+1=289    5w2-4w-288=0    Factoring,    (5w+36)(w-8)=0    Here, we get two values w=-36/5 or 8.    -36/5 is invalid since lengths must always bepositive.    So, w=8 m and l=2w-1=2(8)-1=15 m 2. Let r=rate for the last 75 mi, then r+5=rate for the first 60mi    ---     From the formula d=rt, where d=distance, r=rate,t=time, we get t=d/r     Since the total time is 8 hr,     75/r + 60/(r+5)=8     Adding the fractions,     (135r+375)/(r2+5r)=8     8(r2+5r)= 135r+375     8r2

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