Juyi just got back from a 10 mile bicycle ride. if she had ridden 3 miles per hour faster, the ride would have taken her 30 fewer minutes. wat was her speed on the ride?

Step-by-step explanation:

Let her actual speed = r

Let her actual time = t

d = 10 in either case

Case 1

r*t = 10

Case 2

(r + 10)(t - 1/2) = 10 Note that 30 minutes = 1/2 hour. Remove the brackets

rt + 10t - (1/2) r - 5 = 10

rt = 10 from Case 1

10 + 10t - r/2 - 5 = 10        Subtract 10 from both sides

10t - r/2 - 5 = 0                 Add 5 to both sides

10t - r/2 = 5                      Let t = 10/r from the first equation

10*10/r - r/2 = 5                Simplify the left

100/r - r/2 = 5                   Multiply both sides by 2r

100*2r/r - 2r*r/2 = 5*2r    Simplify

200 - r^2 = 10*r                Subtract 10r from both sides.

-r^2 - 10r + 200 = 0          Use the quadratic formula

a = - 1

b = - 10

c = 200

I'll the quadratic solution to you. The two answers you get are

x1 = -20 (which cannot be used)

x2 = 10 which is the answer

So her rate was actually 10 miles / hour which is a pretty good clip for a bicycle.

explanation:

step-by-step explanation: