South Central High Students’ Council is traveling to Redding for the Students’ Council National Conference. From the travel budget allowed f

Question

South Central High Students’ Council is traveling to Redding for the Students’ Council National Conference. From the travel budget allowed for the trip, they have two options. They can leave by express train tonight, or they can save one hour by leaving tomorrow morning and flying which travels 40 km/h faster than the train. If the distance between South Central High and Redding is 480 km, determine how long it will take to travel by flying, rounded to the nearest hour.

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Melanie 2 weeks 2021-10-03T14:52:37+00:00 2 Answers 0

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    0
    2021-10-03T14:53:56+00:00

    Step-by-step explanation:

    Below is an attachment containing the solution.

    0
    2021-10-03T14:54:19+00:00

    Answer:

    3 hours

    Step-by-step explanation:

    Distance between South Central High and Redding = 480km

    Distance= Average Speed X Time

    Let the speed of the express train=x

    Let the time taken BG the train=t

    For the train:

    480=xt…(1)

    Since the plane flies 40km/hr faster

    Speed of the Plane=x+40

    They can save one hour using the plane, so Time taken by the plane

    =(t-1)hours

    For the plane:

    Distance= Average Speed X Time

    480=(x+40)(t-1)….(2)

    Equate equations 1 and 2 since the distances are equal.

    xt=(x+40)(t-1)

    xt=xt-x+40t-40

    x=40t-40

    Substitute x=40t-40 into equation (1)

    480=xt

    480=(40t-40)t

    40t²-40t-480=0

    Dividing all through by 40

    t²-t-12=0

    t²-4t+3t-12=0

    t(t-4)+3(t-4)=0

    (t-4)(t+3)=0

    t-4=0 or t+3=0

    t= 4hours (Since t cannot be negative)

    Since it will take (t-1) hours to fly, it takes 3 hours to fly to Redding.

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