A boy rides a bike 8 miles. The trip would have taken 20 minutes less if he had ridden 2 miles per hour faster. Find his actual speed.

Question

Algebraic question, possibly including the discriminant and/or quadratic formula, because this question was under the quadratic formula category.

Answer 1

Let us work with hours and mph only.  

 

20 min = 1/3 hour

 

d = vt

 

Slow trip:

 

 8 miles = vt

 

Faster trip:

 

8 miles = (v + 2)(t - 1/3)

 

Solve the system of equations:

 

vt = 8

(v + 2)(t - 1/3) = 8

 

t = 8/v

 

(v + 2)(8/v - 1/3) = 8

 

8 - v/3 + 16/v - 2/3 = 8

 

-v/3 + 16/v - 2/3 = 0

 

Multiply through by -3v and get

 

v^2 + 2v - 48 = 0 

 

v = (1/2) {-2 ± √[(2)^2 - 4(1)(-48)] = (1/2)(-2 ± 14)

 

v > 0, so use positive square root

 

v = (1/2)(-2 + 14) = 6 mph

 

t = 8/v = 8/6 = 1.333 hours