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making linear equation from word problem

An airspeed indicator on aircraft is affected by changes in atmospheric pressure at different altitudes. A pilot can estimate the true airspeed by observing the indicated airspeed and adding it about 2% for every 1,000 feet of altitude.

(a) If pilot maintains a constant reading of 200 miles per hour on the airspeed indicator as the aircraft climbs from sea level to an altitude of 10, 000 feat, write linear equation that expresses true airspeed T (miles per hour) in terms of altitude A (thousands of feet)

(b) what would be the true airspeed of the aircraft at 6,500 feet?

  • algebra -

    T in terms of A is alike to Y in terms of X for linear graphs, so set it up the same way.
    T = (something)A + constant

    The constant reading is 200 miles per hour so that is your constant.
    T = (something)A + 200

    The true airspeed is increasing by 2% or .02 of the indicated reading (constant) for every 1000ft (A). This means you must multiply the percent (.02) by the constant to get the increase per 1000ft (A). [multiply 'A' by this constant for every 1000ft]
    T = 200*(.02)*A + 200

    Reduced: T = 4*A + 200(mph)
    (2)to find the true airspeed at 6500ft simply divide it by 1000 then plug it into the equation.
    T = 4*(6.5) + 200
    T = 226(mph)

  • algebra -

    Thank you so much

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