danzig wrote:

The number of straight line miles traveled downriver in one hour by Lucy's boat is approximated within a linear range by 3n + 4, where n represents her fuel consumption in units/hr. Suppose that traveling x miles requires k hours at a fuel rate of 7 units/hr, but that increasing her fuel consumption by 5 units/hr would allow her to travel 40% further in 1 fewer hour. How far would she travel in k hours at a fuel rate of 10 units/hr?

A. 8

B. 200

C. 225

D. 236

E. 272

The wording of the question is a little complicated so take it one step at a time.

"The number of straight line miles traveled downriver in one hour by Lucy's boat "

miles driven in one hour gives you speed

"is approximated within a linear range by 3n + 4, where n represents her fuel consumption in units/hr."

So speed = 3n+4 where n is the fuel consumption

"Suppose that traveling x miles requires k hours at a fuel rate of 7 units/hr,"

Speed = x/k = 3*7 + 4 = 25

Distance traveled = 25k

"but that increasing her fuel consumption by 5 units/hr would allow her to travel 40% further in 1 fewer hour. "

Speed = 3*12 + 4 = 40

Distance traveled = 40(k-1) = (7/5)*25k (You multiply by 7/5 because 40% extra distance is traveled in this case)

k = 8

"How far would she travel in k hours at a fuel rate of 10 units/hr?"

Speed = 3*10 + 4 = 34

Distance traveled = 34*k = 34*8 = 272 miles

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Karishma

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