Boston is 200 mi away from NY. It takes me 1 hour less to drive to Boston when I drive 10 mi faster than my normal rate. What is my normal rate?
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Thank you. :)
can u also solve it as 200/x -1 = 200/x+10? I got 40 mi/hr
How did you get 40 from that?
Do you mean
200/(x - 1) = 200/(x + 10)
cross multiply
200(x + 10) = 200(x - 1)
200x + 2000 = 200x - 200
NO solution to this
To find your normal rate, we can set up a system of equations:
Let's say your normal rate is x mph.
Since it takes you 1 hour less to drive to Boston at a speed of x + 10 mph, we can set up the equation:
200/(x + 10) = 200/x - 1
Now let's solve for x:
To get rid of the fractions, we can multiply both sides of the equation by x(x + 10):
200x = 200(x + 10) - x(x + 10)
Expanding both sides of the equation:
200x = 200x + 2000 - x^2 - 10x
Combining like terms:
0 = -x^2 + 10x + 2000
Rearranging the equation:
x^2 - 10x - 2000 = 0
Now, we can use the quadratic formula to solve for x:
x = (-(-10) ± √((-10)^2 - 4(1)(-2000))) / (2(1))
Simplifying:
x = (10 ± √(100 + 8000)) / 2
x = (10 ± √8100) / 2
x = (10 ± 90) / 2
Taking the positive root:
x = (10 + 90) / 2
x = 100 / 2
x = 50
Therefore, your normal rate is 50 mph.