Rational Equations Work and Motion Aplications

Question

Hope can bicycle 66 miles in the same time as it takes her to walk 18 miles. She can ride 8 mph faster than she can walk. How fast can she walk?

Using r as your variable to represent the rate at which she walks, write an equation using the information as it is given above that can be used to solve this problem.

Equation: ________________

Hope Walks_______mph

Round your answer to 3 decimal places as needed.

Answer 1

distance = rate×time

d=rt

Walking: rt=18

t = 18/r

Bicycling:

(r+8)t = 66

t = 66/(r+8)

Since the time is the same for both

18/r = 66/(r+8)

18(r+8)=66r

18r+144=66r

48r=144

r = 144/48 = 3 mph

Answer 2

She can bike 66 miles in the same time as she can walk 18 miles. Also, the bike's rate is 8 mph faster than she can walk.

So t_b = t_w and r_b = r_w + 8

D= rt, so t = D/r

t_w = 18/r_w; t_b = 66/r_b

So 18/r_w = 66/r_b Cross-multiply

18r_b = 66r_w Now substitute: 18(r_w + 8) = 66r_w Use distributive property

18r_w + 144 = 66r_w; 48r_w = 144; r_w = 144/48 = 3 mph and r_b = 11 mph (3 + 8)

Walking time is 18/3 = 6 hrs; biking time is 66/11 = 6 hrs (Check!)