Math Help - piecewise problem

A man walks for 45 minutes at a rate of 3 mph, then jogs for 75 minutes at a rate of 5 mph, then sits and rests for 30 minutes, and finally walks for 1 hour and half.Find the rule of the function that expresses this distance traveled as a function of time [ Caution: Don't mix up the units of time ; use either minutes or hours , not both]

could someone help me with this problem? I sketched the graph .the ranges I got are from 0 to .75 , .75 to 2, 2 to 2.5 and 2.5 to 4 .However, I don't know how to write the rules.


Thanks in advance.

Here are some hints for you graph.

We're graphing distance as a function of time. So the x axis should represent time, and the y axis should represent distance.

You know the "rate" at which distance is changing. This rate should be the _____ of your function for a certain time (do you know which word goes in the blank?).


Bonus hint in case you don't know the word:

d = 3t (this is a formula for a man who is walking at 3 miles per hour).

well, I alredy know the 1st and 3rd rule, but I'm still triying to get the other two ones.