easy math for others and hard for me! EXAMS ARE TOM!!?

Question

A team of alaskan sled dogs hauled freight 20 miles.if it had taken them 2hours longer,the distance traveled per hour would have been 5/6 of a mile less. How long did it take them?

+the answer isnt 118 hrs

please!!

Answer 1

time= 6 hours

Ok this is what i did

you have 2 equations (let s=original speed and t= original time)

Distance = speed * time

therefore

20=st

and then you have your conditions (speed decreased time increased) to get another equation

20 = (s-5/6) * (t+2)

Expand

20 = st - (5/6)t + 2s - (10/6)

As we know that st=20 (from the first equation) we can replace this into this equation for st

20=20 - (5/6)t + 2s - (10/6)

0 = - (5/6)t + 2s - (10/6)

Replace s using 20=st .. or s=20/t

0 = - (5/6)t + 2(20/t) - (10/6)

Multiply whole equation by t to get rid of the /t

0 = - (5/6)t^2 + 40 - (10/6)t

A bit of rearranging the numbers to get it neater (you don't have to do this you can just use the equation solve quadratics but its easier if you do)

t^2 + 2t - 48 = 0

(t-6)(t+8)=0

t= 6 or -8 It can't be -8 so it must be 6