The function d(x) = 1375 − 110x represents the distance (in miles) a high-speed train is from its destination after x hours. (section 3.3) a. how far is the train from its destination after 8 hours? b. how long does the train travel before reaching its destination?

If the function d(x) = 1375 − 110x represents the distance (in miles) a high-speed  train is from its destination after x hours:

a) The train is 495 miles from its destination after 8 hours

b) It will take the train 12.5 hours to travel before reaching its destination

The given function is:

d(x)  =  1375  -  110x

Where d(x) is the distance (in miles) a high-speed  train is from its destination after x hours.

a) How far is the train from its destination after 8 hours?

To find how far the train is from its destination after 8 hours, substitute x = 8 into d(x)  =  1375  -  110x

d(8)  =  1375  -  110(8)

d(8)  =  1375  -  880

d(8)  =  495

The train is 495 miles from its destination after 8 hours

b) How long does the train travel before reaching its destination?

Note that:

d(x)  =  1375  -  110x

From the equation above, the speed at which the train is traveling is 110 miles/hr

The distance of the destination = 1375

The time it will take to reach the destination will be calculated as:

Time = Distance / speed

Time = 1375 / 110

Time = 12.5

It will take the train 12.5 hours to travel before reaching its destination

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