Answer:
54 mph
Step-by-step explanation:
we know D = RT, where
D is distance
R is rate/speed
T is time
Normally:
D = RT
378 = RT
This week:
D = RT
378 = (R+9)(T-1)
These are the 2 equations we can write:
Let's mutliply out the last equation:
378 = (R+9)(T-1)
378 = RT - R + 9T - 9
387 = RT - R + 9T
we know RT = 378 and T = 378/R, we replace:
387 = 378 - R + 9(378/R)
9 = -R + 3402/R
Now solving:
[tex]9 = -R + \frac{3402}{R}\\R-\frac{3402}{R}+9=0\\R^2+9R-3402=0\\R=-63,54[/tex]
R can't be negative, so we take R = 54 miles per hour
