A constant rate of salt spreading calls for a linear model: the amount left drops by the same number of tons each mile. Find that rate from the two known markers, then write a rule anchored at one of them. In Desmos, find the marker where the rule reaches zero. Don’t confuse miles traveled after a marker with the marker number.
Hints
- Hint 1
A rate compares the salt used with the distance traveled. Find the drop in tons between the two given markers, then divide by the miles between them. How much salt is used per mile?
- Hint 2
The tons belong at mile marker , not at the warehouse. Start with that amount and subtract the salt used over the miles traveled after marker .
- Hint 3
To run out, the amount remaining must be . If is the salt left at mile marker , what input makes ?
Step-by-step
Build a rule from a known marker
Step 1Find the salt used per mile
From marker to marker , the salt left drops from tons to tons. A rate is the change per mile, so type in Desmos. It shows , or ton used each mile.
- Step 2
Write the remaining-salt rule
Let be the tons left at mile marker . The truck has tons at marker , so counts miles traveled since that marker, not since the warehouse. Start at a known marker, then subtract the amount used over the distance from it. Type in Desmos.
- Step 3
Find where the hopper is empty
Running out means tons left. Type ; the subscript makes the value Desmos finds, and tells it to match the two sides. Under PARAMETERS, Desmos shows . So the truck runs out at mile marker . Choice B.