Question

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?

Answer 1

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!

Answer 2

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.