Question #612

Driving along a crowded freeway, you notice that it takes a time to go from one mile marker to the next. When you increase your speed by 7.4 mph, the time to go one mile decreases by 15 sec. Final answer must be in mph.

Expert's answer

We are asked to find speed in mph:

ν is the speed in mph, Δν=7.4 mph, t1 is the time to go one mile with speed equal to ν, t2 is the time to go one mile with speed equal to ν+Δν:

(1/ν)-(1/(ν+Δν))=15s=0.004167 hours,

(1/ν)-(1/(ν+7.4 mph))=0.004167

ν+7.4 mph-ν=0.004167ν(ν+7.4)

0.004167ν²+7.4*0.004167ν-7.4=0

ν=38.603 mph

ν=-46.003 mph←isn't realistic

Answer:ν=38.603 mph

ν is the speed in mph, Δν=7.4 mph, t1 is the time to go one mile with speed equal to ν, t2 is the time to go one mile with speed equal to ν+Δν:

(1/ν)-(1/(ν+Δν))=15s=0.004167 hours,

(1/ν)-(1/(ν+7.4 mph))=0.004167

ν+7.4 mph-ν=0.004167ν(ν+7.4)

0.004167ν²+7.4*0.004167ν-7.4=0

ν=38.603 mph

ν=-46.003 mph←isn't realistic

Answer:ν=38.603 mph

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