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A GCSE Maths question

Here are a few parts of a question i found on a past edexcel GCSE maths paper; i'm struggling...

Fred cycled from home to his friend's house and back again.
The distance from Fred's home to his friends's 'home is 20KM.
On his way from home to his friend's house, fred cycled at X km per hour.
On his way back, Fred's speed had decreased by 2km per hour.
It took Fred 4 hours altogether to cycle to his friend's house and back.

(A) Write down an equation for X.
?? X=20/4-2 ??

(B)Show that the equation can be written as: x2-12x+10=0
???

(C) Solve the equation in part B

(D) Only one of the answers in part C can be Fred's speed, explain why.

Sorry for the long-winded question. Thanks in advance for any help provided.

Reply 1

Krazof

For part a) make simultaneous equations, one for the way there and one for the way back. Do you see where they have come from?

Unparseable latex formula:

s = \frac{d}{t}\\[br]\\[br]x = \frac{20}{t}\\[br]\\[br](x - 2) = \frac{20}{4 - t}

Reply 2

Beccajh

(A) Use your knowledge of distance under graph = distance travelled

(B) Expand out and rearrange, not attemted to question yet, but I can't quite see where the other X came from, but I'm sure it's possible

(C) Do you know how to solve quadratic equations? Get it into 2 bracket and you'll get 2 answers (at least one of the brackets must = 0) the positive answer is correct. (If this sounds foreign to you, look it up! you need to know it for GCSE)

(D) Half answered above... I'll leave you to try to work out why!

Try and do it from those hints, I will give you more if you get stuck