# Question 9b1bc

Feb 7, 2018

$36$ seconds

#### Explanation:

Obviously, adding together the times wouldn't make sense, since that would mean it takes longer for him to travel up the escalator when he is moving faster.

So, we need to instead add together the speeds of both the man by himself, and the escalator by itself, in order to get the combined speed of the two of them together.

Speed, or velocity, is measured in distance units divided by time units. In this case, our distance unit is "escalator lengths", and our time unit is seconds.

By himself, this man walks at a speed of (1 " escalator")/(90 " seconds") = 1/90 "escalators"/"second"

By itself, the escalator moves at a speed of (1 " escalator")/(60 " seconds") = 1/60 "escalators"/"second"#

Therefore, if the man walks while the escalator is moving, the combined speed of the man and the escalator will be:

$\frac{1}{90} \text{escalators"/"second" + 1/60 "escalators"/"second}$

$= \frac{2}{180} \text{escalators"/"second" + 3/180"escalators"/"second}$

$= \frac{5}{180} \text{escalators"/"second}$

So he can travel 5 "escalator lengths" in 180 seconds. This means that to travel just ONE escalator length, it will take him:

$\frac{180}{5} \text{ seconds" = 36 " seconds}$