help me please

Question

Fred cycled from home to his friend's house and back again.The distance between their houses is 20km.On his way to his friend's house, Fred cycled at x km/h.on the way back, Fred cycled 2 km/h slower. It took Fred 4 hours altogether to cycle to his friemd's house and back.  

 

find an equation for x?

show that the equation  can be written as x^2-12x+10=0

Answer 1

Heading out to his friend's house, it takes Fred t hours at speed x to travel 20 km:

 

xt = 20

 

Returning home, it takes him t' hours at speed x-2 to travel the same 20 km:

 

(x-2)t' = 20

 

Total round trip time is 4 hours:

 

t+t' = 4, so t' = 4-t

 

So now we have 2 equations in 2 unknowns:

 

xt = 20

(x-2)(4-t) = 20

 

The top equation gives t = 20/x.  Substitute this into the bottom equation and obtain an equation in x:

 

(x-2)(4 - 20/x) = 20

 

Multiply both sides by x:

 

(x-2)(4x-20) = 20x

 

Expand and simplify to obtain final equation in x:

 

x² -12x + 10 =0

 

Solve for x, get x-2, and you can also get t.