Answer:
The first rate is 6 miles per hour
The final rate is 6+2 or 8 miles per hour
Step-by-step explanation:
We know d = rt where distance is equal to rate times time
First part
d1 = r * 1/3
Second part
d2 = (r+2)(3/4)
We know the total distance is 8 miles and is
d1+d2 = 8
r * 1/3 + (r+2)(3/4) = 8
Multiply each side by 12 to get rid of the fractions
12( r * 1/3 + (r+2)(3/4)) = 8*12
4r +(r+2) 9 = 96
Distribute
4r+ 9r +18 = 96
Combine like terms
13r +18 = 96
Subtract 18 from each side
13r+18-18 = 96-18
13r = 78
Divide each side by 13
13r/13 = 78/13
r=6
The first rate is 6 miles per hour
The final rate is 6+2 or 8 miles per hour
