Answer:
s - 20 = 60 km/hr
Step-by-step explanation:
The distances are the same going there and coming back.
So
Givens
d = 400
2/5 * d = 2/5 * 400 = 160
The rest of the trip back = 400 - 160 = 240
Equation
400/(s) + 160/s + 240/(s - 20) = 11 hours.
Solution
distance / speed = time or
d/s = time
Multiply through by s*(s - 20)
400*(s - 20) + 160*(s - 20) + 240s = 11*s*(s - 20) Remove the brackets.
400s - 8000 + 160s - 3200 + 240s= 11(s^2 - 20s) Collect like terms on the left.
560s - 11200 + 240s = 11(s^2 - 20s) Remove the brackets on the rt.
800s - 11200 = 11s^2 - 220s Switch and add 220s
11s^2 - 220s + 220s = 800s +220s - 11200 Combine
11s^2 = 1020s - 11200 Put everything on the left.
11s^2 - 1020s + 11200 = 0
this quadratic factors into
(11s - 140 )(s - 80) = 0
You have 2 solutions
11s - 140 = 0
11s = 140
s = 140/11
s = 12.727272... This solution won't work because the speed has no room to drop down 20 km / hour
===========
s - 80 = 0
s = 80 km hour
But that is not the answer
=======
The answer you want is s - 20 which is 60 km/hr.
