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Answer:
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
When the cable car’s elevation will be 750 feet after minutes, then we have
Time cannot be negative, so the cable car’s elevation will be 750 feet after 15 minutes or 65 minutes.