Question

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?

Answer 1

d(x) = 1375 - 110x.....where x is the hrs traveled and d(x) is the distance in miles left to travel

(a) after 8 hrs....so x = 8
     d(8) = 1375 - 110(8)
     d(8) = 1375 - 880
     d(8) = 495...so after 8 hrs, u r 495 miles short of ur destination

(b) before reaching its destination...its destination is 1375 miles....and if u r traveling 110 miles per hr....1375/110 = 12.5....so after 12.5 hrs, u should reach ur destination.

Answer 2

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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