Answer:
a) It takes Samantha 12 minutes to walk 1 mile
b) It takes Tina 6 minutes to bike 1 mile
c) k(t) = 0.083t
d) m(t) = 0.167t
e) Tina arrives befora Samantha
Step-by-step explanation:
a) How many minutes does it take Samantha to walk 1 mile?
This is a direct rule of three problem. So:
6 minutes - 0.5 miles
x minutes - 1 mile
x = 6/0.5 = 12 minutes
It takes Samantha 12 minutes to walk 1 mile
b) How many minutes does it take Tina to bike 1 mile?
Quite similar to a)
1.5 minutes - 0.25 miles
x minutes - 1 mile
x = 1.5/0.25 = 6 minutes
It takes Tina 6 minutes to bike 1 mile
c) Write a function k that determines the number of miles Samantha has walked in terms of the number of minutes.
We know that it takes 6 minutes for Samantha to walk 0.5miles. To build our function k, we need to know how many miles Samantha walks a minute.
So
6 minutes - 0.5 miles
1 - minutes - x miles
x = 0.5/6 = 0.083 miles
So the number of miles in function of t is
k(t) = 0.083t
d) Write a function m that determines the number of miles Tina has biked in terms of the number of minutes since she started biking
Same logic as c). So:
1.5 minutes - 0.25 miles
1 minute - x miles
x = 0.25/1.5
x = 0.167
So the number of miles in function of t is:
m(t) = 0.167t
e)
Samantha will arrive when k = 1.3, so:
0.083t = 1.3
t = 15.66 minutes
Tina will aririve when m = 2.5, so:
0.167t = 2.5
t = 14.9 minutes
Tina arrives befora Samantha
