Answer:
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.
Answer:
Step-by-step explanation:
Speed-r
Time-t
r*t = 10
(r + 10)(t - 1/2) = 10
rt + 10t - (1/2) r - 5 = 10
rt = 10
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:
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
a = - 1
b = - 10
c = 200
x= -20
x = 10
Since you can't go a negative number of miles per hour, her speed was 10 miles per hour.
Hope this helps!
