can you use time=distance/speed with this problem?

Question

A woman can bicycle 68 miles in the same time as it takes her to walk 12 miles. She can ride 7 mph faster than she can walk. How fast can she walk?

Answer 1

we know that speed=distance/time 

ie time = distance /speed

 

let her speed be 'u' when she is riding the bike and be'v' when walking.

as per the question we have   u=7+v

also we have that time taken to ride bike for 68 miles is same as time to walk 12 miles.

time in riding the bike = 68/u 

time in walking = 12/v

these times are equal so

68/u= 12/v

so 68 v=12 u

but  u=v+7 

so 68 v= 12 (v+7)

68 v= 12v +84

56 v=84 

so v is 84/56 

v= 21/14= 1.5 miles/hr

Answer 2

d=rt

12=rt

68=(r+7)(t)

from 12=rt, 12/r=t

substitute

68=(r+7)(12/r)

multiply both sides by r

68r=(r+7)(12)

68r=12r+84

68r-12r=84

56r=84

r=84/56

r=1.5 mph walking (answer)

r+7=8.5 mph riding

12=1.5*t  and 68=8.5*t

12=1.5*t, t=8 hours, 68=8.5*8