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Ok, I'm doing a Mock End of Unit Test Revision paper and I'm stuck on a few questions.

The first question is:

Susan completes the journey in $2$ stages of her journey. In stage 1 of her journey, she drives at an average speed of $80$km/h and takes $1$ hour and $45$ minutes.

(a) How far does she travel?

I know that answer is $140$ because:

$1$ hour $=$ $80$km/h

A quarter of $80$ ($15$ minutes) is $20$ and I need three-quarters as there's $45$ minutes which is $60$.

$80$ $+$ $60$ $=$ $140$. I know it's the right answer however how come on the Marking Paper the method of working it out is doing $80$ x $1.75$. Where do you get $1.75$ from?

Second question:

Altogether Susan travels $190$km/h and takes the total time of $2$ hours and $15$ minutes.

(b) What is her average speed, in km/h, in stage $2$ of her journey?

I know that you would start of by doing $190$ $-$ $140$ = $50$. I'm not sure what to do after that though. Thanks everyone, I know it seems quite easy.

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  • $\begingroup$ $1$ Hour $45$ Minute =$1+\frac{45}{60}$ Hours $\endgroup$ – lab bhattacharjee Oct 25 '13 at 15:56
  • $\begingroup$ umm I still don't know where the $1.75$ is from. $\endgroup$ – user61406 Oct 25 '13 at 15:59
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    $\begingroup$ $$\frac{45}{60}=\frac34=0.75$$ $\endgroup$ – lab bhattacharjee Oct 25 '13 at 16:02
  • $\begingroup$ When you write "1 hour = 80 km/hr" this does not make sense. You are trying to say that she covers 80 km in the first hour. $\endgroup$ – Ross Millikan Oct 28 '13 at 13:30
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For question $a$, $1.75$ is how many hours it takes for the journey (note that $45$ minutes = $0.75$ hours). For question $b$, the average speed is $\frac{distance}{time} = \frac{190-140}{2.25-1.75} = \frac{50}{0.5} = 100$ km/h. In words, in the second part a distance of $50$ km is travelled in $30$ minutes, so the average speed is $100$ km/h.

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  • $\begingroup$ I understand but why is $45$ $=$ $0.75$? $\endgroup$ – user61406 Oct 25 '13 at 16:01
  • $\begingroup$ $45$ minutes is three quarters of an hour, and three quarters is $0.75$. Alternatively, divide $45$ by the number of minutes in a full hour ($60$) to get $0.75$. $\endgroup$ – Arthur Oct 25 '13 at 16:01
  • $\begingroup$ Ahh, didn't realise. Thanks. $\endgroup$ – user61406 Oct 25 '13 at 16:02
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"A quarter of 80 (15 minutes) is 20 and I need three-quarters as there's 45 minutes which is 60."

Translated into an equation this is what you did:

Distance traveled in 45 mins = (Distance traveled in 15 mins) * 3

But, (Distance traveled in 15 mins) = 80/4 (since 15 mins is 1/4th of an hour

Thus,

Distance traveled in 45 mins = (80/4) * 3 = 80 * (3/4)

Therefore, total distance traveled = 80 + 80 * (3/4) = 80 * 1.75

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  • $\begingroup$ oh ok, I understand now thanks. $\endgroup$ – user61406 Oct 25 '13 at 16:10

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