A recent report from the government explained that as you increase your speed fr

Question

A recent report from the government explained that as you increase your speed from 50 MPH to 60 MPH, your fuel efficiency (number of mile per gallon) decreases by 12.4%; as you increase your speed from 60 MPH o 70 MPH, your fuel efficiency fuel decreases by 15.4%. A journalist, assed the percerntages and concluded that as you increase your speed from 50 MPH to 80 MPH your fuel efficiency decfeases by 41.8%. Determine what is the correct decrease in fuel efficiency as you increase your speed from 50 MPH to 80 MPH.

Explanation / Answer

let the efficiency be=E

increase your speed from 50 MPH to 60 MPH the efficiency becomes=E-12.4*E/100=0.876E

let,

0.876E=x

increase your speed from 60 MPH to 70 MPH the efficiency becomes= x-15.4*x/100=0.846x

but x=0.876E

so total decrease in efficiency from 50MPH to 80MPH=0.846*0.876E=0.741096E

the total decrease in percentage=[(E-0.741096E)/E]*100=25.8904%

25.8904% is correct decrease in efficiency and the journalist is wrong

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