Question

A car travels at a constant speed of 60km/hr for 1.5 hours, stops for half an hour then travels for another 2 hours at a constant speed of 80km/hr, reaching it's destination.
a) Construct a function that describes the distance travelled by the car, d (km), at time, t hours.
b) State the domain and range of this function
c) Calculate the distance travelled after 3 hours

Will give medal and fan!!

Answer 1

@Hero
@dan815

Answer 2

This function will change depending on the domain (the value of t).

\[d=60t \space \space \space \space \space for \space 0\le t < 1.5\]\[d=60 \times 1.5 = 90 \space \space \space \space \space for \space 1.5\le t < 2\]\[d=80(t-2) \space \space \space \space \space for \space 2 \le t \le 4\]
All three of these functions together represent the function d(t)...I just don't know how to make a fancy bracket to point all of them to one d :P

You get the first part of the function simply by multiplying speed by time to give you distance, which is the case for the first 1.5 hours of the trip. The second part of the function represents the half hour the car is stopped - it doesn't cover any more distance, so the distance traveled during this time is equal to the distance traveled during the first 1.5 hours. The third part of the function is a bit tricky - again you're multiplying speed by time, but this time you have to take into account the fact that the car is only traveling at this rate for the last 2 hours (hence the t-2 instead of just t).

The domain is 0 ≤ t ≤ 4 and the range is what you get if you plug those numbers into the appropriate parts of the equation, in this case 0 ≤ d ≤ 320.

After three hours, you're past the first and second parts of the function, so the car has traveled at least 90 km. We can plug in 3 to the third equation, giving us an additional 80 km. 90 + 80 = 170 km, the total distance traveled in the first 3 hours.

Hope that makes sense! if you have any questions please ask!

Answer 3

That definitely makes sense. Thank-you so much :) @matt101