Answer: [tex]e=-50|t-40|+2000[/tex]
The cable car’s elevation will be 750 feet after 15 minutes or 65 minutes.
Step-by-step explanation:
Given: A cable car begins its trip by moving up a hill. As it moves up, it gains elevation at a constant rate of 50 feet/minute until it reaches the peak at 2,000 feet.
Then, total time taken to reach the peak = (Distance) ÷ (speed)
= (2,000 feet) ÷ ( 50 feet/minute)
= 40 minutes
Then, as the car moves down to the hill’s base, its elevation drops at the same rate.
The equation that models the cable car’s elevation, e, after t minutes is
e= (constant rate)|t- time to reach peak |+ Peak's height
[tex]e=-50|t-40|+2000[/tex]
When the cable car’s elevation will be 750 feet after minutes, then we have
[tex]750=-50|t-40|+2000\\\\\Rightarrow\ -50|t-40|=750-2000\\\\\Rightarrow\ -50|t-40|=1250\\\\\Rightarrow|t-40|=-\dfrac{1250}{50}\\\\\Rightarrow|t-40|=-25\\\\\Rightarrow t-40=-25\text{ or }t-40=25\\\\\Rightarrow t=-25+40\text{ or }t=25+40\\\\\Rightarrow t=15\text{ or }t=65[/tex]
Time cannot be negative, so the cable car’s elevation will be 750 feet after 15 minutes or 65 minutes.
