Problem Solving Help

[katie101]

One alloy of iron contains 52% iron and another contains 36% iron.

How many tonnes of each alloy should be used to make 200 tonnes of 40% iron alloy?

[IndefatigableLover]

So one way in which you could work this out is through simultaneous equations.
If we label both irons as 'x' & 'y' then we know that for one equation that it has to be:

Spoiler

X + Y = 200 (X & Y are the weights of the iron and the tonnes of each alloy will add up to 200 tonnes).

Now we also know that each alloy is respectively 52% and 36% which can be expressed as

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0.52x & 0.36y

Because of that, we also know that it must all have a 40% iron alloy so then it would look like:

0.52x + 0.36y = 0.40Z

And luckily we know what 'z' is (which is 200 tonnes) so our two simultaneous equations are:

X+Y = 200 (1)
0.52x + 0.36y = 80 (2)

I think from there you could solve it all out (probably best if you made equation (2) into whole numbers rather than with decimals )

[katie101]

Great thanks!

Also I'm having difficulty with this one
......................

A car leaves Melbourne at 8am travelling at a constant speed of 80km/h.
It is followed at 10am by another car travelling on the same road at a constant speed of 110km/h.
At what time will the second car overtake the first?

[brightsky]

Draw a velocity-time graph and then find the t coordinate at which the area under each curve is identical. Note that the area represents distance travelled.

[IndefatigableLover]

This one was a bit more trickier for me but I 'think' I've got the answer!

So Let's say Car 1 = 8am and Car 2 is 10am.

Car 1 leaves at 8am and by 10am it is already:

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160km away from Car 2 when it starts

Since Car 2 is playing catch up, we can just use this to find how much time it takes for Car 2 to catch up to Car 1:

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Distance travelled by Car 2 - Distance travelled by Car 1 = 160km

This can be substituted for this equation:

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110t - 80t = 160, where 't' is equal to time.

From here we can work out how much time it takes for Car 2 to overtake Car 1!

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30t = 160

= 5.333 hours (same as 5 and one-third)

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If you want to convert from hours to minutes then simply multiply the final answer by 60 to get it into minutes

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which happens to be 320 minutes

And remember to state your answer since it's a worded question rather than leaving it as 't' = ....

SO:

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320 minutes after 10am is 3:20pm (if I'm not mistaken) so that means that the second car will overtake the first one after 3:20pm.

[Zealous]

A car leaves Melbourne at 8am travelling at a constant speed of 80km/h.
It is followed at 10am by another car travelling on the same road at a constant speed of 110km/h.
At what time will the second car overtake the first?

Let t=amount of hours after 8am.

The first car would have travelled the distance 80t, which is 80km/h multiplied by how many hours it has been travelling for.

The second car would have travelled the distance 110(t-2), which is 110km/hour multiplied by how many hours it has been travelling for minus 2 hours (this is because the second car started 2 hours after the first car).

Equate the two expressions (we want the distance to be the same):









That is, 22/3 hours after 8am, the two cars would be at the same point. 22/3 hours after 8am is 3:20pm.

[katie101]

Thanks all

Yep, the correct answer is 3:20pm!

[alchemy]

One alloy of iron contains 52% iron and another contains 36% iron.

How many tonnes of each alloy should be used to make 200 tonnes of 40% iron alloy?

I'd usually start off making a table like this to make sure I don't make a mistake. It's almost exactly the same as Indefatigable Lover's method but doesn't include the variable y that isn't needed. Hence, you don't need to solve simultaneous equations at the end and can probably do the final steps by hand

Both these quantities should add up to 200 tonnes of the 40% iron alloy. So:

Hence, .

[katie101]

Thanks

Would you be able to tell me what method I should use to solve this problem
...........
Determine all the values for k so that the quadratic expression x^2+kx-19 can be factorised using intergers.

I've seen these before but I haven't been taught how to complete.
Thanks

[alchemy]

Determine all the values for k so that the quadratic expression x^2+kx-19 can be factorised using intergers.

I've seen these before but I haven't been taught how to complete.
Thanks

Hint: Use the discriminant (b²-4ac).

Otherwise, notice the middle term can be expressed as a product of the coefficient of a and c.  In this case it's 1 and 19.
So k can be either 1-19=-18 or 19-1=18.

[katie101]

Aweomse, using the discriminent makes it easier
Thanks

[alchemy]

Aweomse, using the discriminent makes it easier
Thanks

Haha, yeah that's what most use. The other method is slightly quicker though but dw about it, I guess.

[katie101]

I get that way as well, but is it safer to use the discriminent? 

[alchemy]

I get that way as well, but is it safer to use the discriminent?

Well tbh it's using the discriminate is a longer way that happens to be more laborious. With complexity comes the chance to make a mistake. I'd stick with the second method to be 'safe', but both are fine.