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How do I do this question? Thanks!

J.-E. Pin
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Jamie A
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2 Answers2

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$$ \text{distance} = \text{rate}\times\text{time}. $$ Therefore $$ \text{time} = \frac{\text{distance}}{\text{rate}}. $$ So $$ \text{total time} = \frac3x+\frac{3}{x+1}. $$ That's an "expression for the total time". You can't get a concrete number because $x$ could be any speed at all.

Michael Hardy
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  • Great! Thank you. I completely understand that, but what about these? I'm a little confused. http://cl.ly/SCQP – Jamie A Oct 28 '13 at 17:44
  • If the total time is known to be $2$ hours, then you'd have $2 = \dfrac3x+\dfrac{3}{x+1}$. Multiplying both sides by $x(x+1)$, on the left side you'd get $2x(x+1)$. On the right side you'd get $\dfrac3x x(x+1) + \dfrac{3}{x+1}x(x+1)$. In the first fraction, the $x$ cancels and in the second, $x+1$ cancels, and you get $3(x+1)+3x$. So you have $2x(x+1)=3(x+1)+3x$. This simplifies to $2x^2+2x=6x+3$, and then to $2x^2-4x-3=0$. ${}\qquad{}$ – Michael Hardy Oct 28 '13 at 17:49
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In order to answer this question, you need a few ingredients. First, if the slug is moving at constant speed $v$ for a time $t$, it will cover a distance $d = vt$.

Second, you should solve this formula for $t$, giving $t = \frac{d}{v}$.

Hence, the time the slug takes on the first three miles, going $x$ mph is $\frac{3}{x}$ hours and similarly, the time the slug takes on the second three miles, going $x + 1$ mph is $\frac{3}{x + 1}$.

Hence, the answer to your question is $\frac{3}{x} + \frac{3}{x+1}$.

Theo
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  • Great! Thank you. I completely understand that, but what about these? I'm a little confused. http://cl.ly/SCQP – Jamie A Oct 28 '13 at 17:45