# Thread: Speed, distance etc

1. ## Speed, distance etc

Fred cycled from home to his friends house and back again.
The distance is 20km.
On his way home, he cycled x km per hour.
On his way back, his speed decreased by 2km per hour.
It took him 4 hours altogether to cycle to his friends house and back.

1. Write down an equation for x

x = (20/4) - 2 ?

2. Show that the equation can be written as x^2 - 12x + 10 = 0
3. Solve the equation in question 2 to 1 decimal place
4. Only one of teh answers in question 3 can be Freds speed. Explain why.

2. Originally Posted by GAdams
Fred cycled from home to his friends house and back again.
The distance is 20km.
On his way home, he cycled x km per hour.
On his way back, his speed decreased by 2km per hour.
It took him 4 hours altogether to cycle to his friends house and back.

1. Write down an equation for x

x = (20/4) - 2 ?

2. Show that the equation can be written as x^2 - 12x + 10 = 0
3. Solve the equation in question 2 to 1 decimal place
4. Only one of teh answers in question 3 can be Freds speed. Explain why.
Hello,

you know that $\displaystyle speed = \frac{distance}{time}$ that means $\displaystyle time = \frac{distance}{speed}$

So you can set up an equation to calculate the time:

$\displaystyle \frac{20}{x} + \frac{20}{x-2} = 4$ . Multiply both sides by x(x-2):

$\displaystyle 20(x-2) + 20x = 4x(x-2)$

$\displaystyle 20x - 40 + 20x = 4x^2 - 8x$

$\displaystyle 4x^2 - 48x + 40 = 0$

$\displaystyle x^2 - 12x + 10=0$

I assume that you know how to solve a quadratic equation. (I've got the solutions: x =11.1 or x = 0.901) It is obvious that the 2nd solution never satisfies the given conditions because Fred would have traveled back with a negative speed

3. I tried using the formula to solve it because I didn't think it could be factorised, bt got different answers:

x = ( -12 + or - sq.rt 12^2 - 4*1*-10 ) / 2

x = ( -12 + or - sq.rt 184 ) / 2

x= -5.22 or -18.78

Arghhhh!

4. Originally Posted by GAdams
I tried using the formula to solve it because I didn't think it could be factorised, bt got different answers:

x = ( -12 + or - sq.rt 12^2 - 4*1*-10 ) / 2

x = ( -12 + or - sq.rt 184 ) / 2

x= -5.22 or -18.78

Arghhhh!
Hello,

you are one sign away from the corect solution:

x = ( 12 + or - sq.rt (12^2 - 4*1*10 )) / 2

x = ( 12 + or - sq.rt 104 ) / 2

x= 11.1 or 0.901