Total Time Expression Question

Question

How do I do this question? Thanks!

Answer 1

$$ \text{distance} = \text{rate}\times\text{time}. $$ 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.

Answer 2

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 $\frac{3}{x} + \frac{3}{x+1}$.