Question

A high speed passenger train travels at 110 mph. The function d(x)= 1375-110x represents the distance (in miles) the chain is from his destination after x hours it is

1. Does this function that describes this scenario leaner or nonleaner?

2.How many more miles does the train have to travel after 8 hours?

3. How many hours has the train traveled if it is 275 miles from its destination?

4. After how many hours will the train reach its destination?

Answer 1

The given function is linear, because it has a constant rate of change (slope) of -110, which means that the distance from the destination decreases by 110 miles for every hour of travel.

To find the distance the train has to travel after 8 hours, we can plug in x=8 into the given function and subtract the result from the initial distance of 1375 miles:

d(8) = 1375 - 110(8) = 695

So the train has to travel 695 miles after 8 hours.

To find how many hours the train has traveled if it is 275 miles from its destination, we can set the distance d(x) to 275 and solve for x:

d(x) = 1375 - 110x = 275

110x = 1100

x = 10

So the train has traveled for 10 hours if it is 275 miles from its destination.

To find after how many hours the train will reach its destination, we can set the distance d(x) to 0 and solve for x:

d(x) = 1375 - 110x = 0

110x = 1375

x = 12.5

So the train will reach its destination after 12.5 hours of travel.