Question

The distance you travel while hiking is a function of how fast you hike and how long you hike at this rate. You usually maintain a speed of three miles per hour while hiking. Write an equation that represents this function, letting t represent the independent variable, let h represent the function, and h(t) the dependent variable. Then, determine h(4).
a.
h(t)(3t/4); 48 miles
b.
t(h)=3h; 12 miles
c.
h(t)=3t; 12 miles
d.
h(t)=(3t/4); 3 miles

Answer 1

C.
A way to remember this is to think about how you cancel out to find your distance.
Your speed is in miles per hour (represented as miles/hour).
You are trying to find miles and they give your speed:
3miles/hour
So in order to end up with just miles, you multiply by time or (t).
h(t)=h*t=ht
so h(t)=3*t,
h(4)=3t
input 4 into t
h(4)=3(4)=12miles

Slightly more detailed explanation:
You know time is the independent variable because no matter how fast you go, time will not change no matter how fast you hike. So in h(t) t is time, and its unit is hr. speed is miles/hr, you multiply to cancel out the hr and just get minutes.

Answer 2

Thank you @lapinblanc

Answer 3

You are very welcome.