Step-by-step explanation:
so, the given ratio is
15 m/s
when we transform this into other quantities, we always have to keep the original ratio "alive". meaning, when we change something to one part of the ratio/fraction, we need to do the corresponding change also for the other one.
when we change a metric of one part, we change only that part, because we are only replacing a number by another number with the same meaning of quantity (and the ratio stays unchanged).
let's start with the easier part : going from 1 second to a full hour as time reference (needed for miles per hour).
this is changing a quantity.
15 m / 1 s
1 hour = 60 minutes, 60 seconds each = 60×60 = 3600 seconds.
so, to bring the ratio to 1 hour instead of 1 seconds, we need to multiply the denominator (1 s) by 3600, and therefore also the numerator by 3600 (again, to keep the ratio alive).
15 m / 1 s × 3600/3600 = 15×3600 m / 3600 s =
= 54000 m / 1 hour
which would be, by the way, 54 km/h.
if we just replaced 1 second by 1/3600 hour, that would be changing the metric while keeping the same quantity information, and we could have done that change only in the denominator.
but we changed the quantity from 1/3600 hour to 1 hour.
and now we need to charge the metric (not the quantity information) of the numerator.
54000 meters are how many miles ?
1 mile ≈ 1609 meters
so, we need to see how often 1609 fits into 54000. and that's our answer for how many miles there are in 54000 meters :
54000 / 1609 = 33.56121815... miles ≈ 33.6 miles
so, the hummingbird travels at up to
33.6 miles per hour
