algebra 2 walking speed

Question

Jaxson walks a 3 miles to house of friend and then rides 9 miles on bike to the store. He averages 4 miles per hours faster when cycling than when walking, and the total time for both trips is 2 hours. Find his walking speed.

Answer 1

3/w + 9/b = 2

b=4+w

distance divided by speed = time traveled

d/w + 9/b = 2

3/w + 9/(4+w) = 2

multiply by w(4+w)

12+3w + 9w = 2w(4+w)= 8w +2w^2

2w^2 -4w -12 = 0

w^2 -2w -6=0

(w^2 -2w +1) = 6+1= 7

w-1 = sqr7

w = 1+sqr7

b = 5+sqr7

walking speed = 1+sqr7 = about 3.65 mph

cycling speed = 5+sqr7 = about 7.65 mph

3/(1+sqr7) + 9/(5+sqr7)=2

3(5+sqr7) + 9(1+sqr7) = 2(1+sqr7)(5+sqr7)

15 +3sqr7 + 9+9sqr7 = 2(5 +6sqr7+7)

24 + 12sqr7 = 24+12sqr7

it's almost 4 and 8 mph, but a little less

rounded off to nearest integer

walking speed = 4 mph

cycling speed = 8 mph

he went 12 miles in 2 hours, averaging 12/2 = 6 mph