Question

WILL FAN AND MEDAL! need help making a problem
Sheldon and Leonard are preparing for their annual trip to Comic-Con, a comic book convention.

After careful analysis of route options, and based on traffic patterns, Leonard determines the following: while driving at a constant pace, they will travel 50 miles in the first hour, 255 miles in the next 3 hours, and 120 miles in the next 2 hours.
Create a piecewise function representing Leonard and Sheldon’s traveling time and distance.

Answer 1

if distance =y and time=x

Answer 2

y is distance and x is time?

Answer 3

yes! @satellite73

Answer 4

ok then for \(0\leq x\leq 1\) you know \(y=50x\) as distance equals rate times time

Answer 5

what is the rate for the next three hours?

Answer 6

255?

Answer 7

on no
that is the total distance for 3 hours
to find the rate, divide 255 by 3

Answer 8

85

Answer 9

wow they are going fast

Answer 10

so so far y=50x+85...?

Answer 11

no you are looking for a piecewise function right?

Answer 12

yess..

Answer 13

going to look something like \[y = \left\{\begin{array}{rcc}
50x & \text{if} & 0\leq x\leq 1\\
50+85x& \text{if} &1<x\leq 4
\end{array}
\right.\]

Answer 14

what is the next rate?

Answer 15

120 miles in two hours?

Answer 16

thats divided by 3?

Answer 17

is what divided by three?

Answer 18

would that be 40?

Answer 19

120 miles in two hours?

Answer 20

oh scuse me sorry, 60?

Answer 21

yes

Answer 22

ok now only one more step
how far have they gone so far?

Answer 23

for the first four hours that is

Answer 24

425 miles

Answer 25

in all?

Answer 26

no for the first four hours

Answer 27

well for the first hr it says 50

Answer 28

yes
and then how far in the next three hours?

Answer 29

305?

Answer 30

yes

Answer 31

so its the equation you wrote down and =305?

Answer 32

\[y = \left\{\begin{array}{rcc}
50x & \text{if} & 0\leq x\leq 1\\
50+85x& \text{if} &1<x\leq 4\\
305+60x&\text{ if} &4<x\leq6
\end{array}
\right.\]

Answer 33

thats the piecewise function?