Alg. 2 Help - Functions?

Question

First of all, please don't answer "Do your homework"

A climber left base camp at 5AM to ascend a 7400-M peak. The climber gained altitude at the rate of 240 m/h and at 8 AM was at the 6500-M level.

a.) Find the elevation of the base camp
b.)At what time did the climber reach the summit?

These have to be described w/ a linear function, not algebraically.

Just to make it clear, it has to be put in A LINEAR FUNCTION , not d=rt, or anything else.

F(X) = MX + B

NOTHING ELSE, just ^

Answer 1

t = hours elapsed since 5AM
elevation = f(t) = 240t + b

At 8AM, t=3 and
f(3) = 720 + b = 6500, so
b = 5780

At 5AM, t=0 so
f(0) = 5780
The elevation of the base camp is 5780m

Find t such that f(t) = 7400:
f(t) = 240t + 5780
240t = 7400 - 5780
t = 6.75
The climber reaches summit at 11:45AM

I hope this satisfies the linear equation requirement.

Answer 2

5 AM Base Camp
6AM Base Camp + 240m
7AM Base camp + 480m
8AM Base camp +720m = 6500 m
So Base camp = 6500- 720 = 5780m
He has another 7400m-6500 m = 900m to go
So it will take another 900/240 = 3.75 hours to arrive at peak
So he will arrive at peak/summit at 11:45AM.
Height = 240t + 5780 where t is time in hours. This is a linear function, but it is also algebraic, so I don't know if I have answered your question.

Answer 3

d=rt
at 8AM time is 3 hours
d=(240)(3)=720 m which is how far he went
so base camp is at 6500-720 or 5780 m level

summit is 7400-5780=1620 m away from base so
1620=(240)t
t=6.75 hours which is 6 hours 45 minutes from 5 AM so time to reach summit is 11:45 AM