# Speed, distance etc

• Jul 3rd 2007, 03:10 AM
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.
• Jul 3rd 2007, 04:09 AM
earboth
Quote:

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 $speed = \frac{distance}{time}$ that means $time = \frac{distance}{speed}$

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

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

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

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

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

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

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 :mad:
• Jul 3rd 2007, 11:36 PM
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!
• Jul 4th 2007, 01:58 AM
earboth
Quote:

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