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syyy
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Tyro
Asked: 2021-03-30T14:24:30+00:00 In: ,

Problem solving using rational algebraic expressions

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A boat is travels 120 km from its home port to a fishing area. On the way back, the boat traves 15 km/hr slower because it has full load. If the return trip takes 1.5 hours longer, what is the total travel time for each trip?

algebra

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  2. acedstud
    This answer was edited.

    The relationship between distance (d), speed (s), and time (t) is by d=st.

    Let the speed taken while going for the fishing be s km/hr, then the speed on the return journey is s-15 km/hr.

    Also, let the time taken while going for the fishing be t hrs, then the speed on the return journey is t+1.5 hrs.

    The distance of both journeys is equal to 120 km, thus 120=st and 120=(s-15)(t+1.5). From the first equation, 120=st, we have s=\dfrac{120}{t}. Substitituting this into the second equation gives 120=\left(\dfrac{120}{t}-15\right)(t+1.5)=120+\dfrac{180}{t}-15t-22.5

    \Rightarrow\dfrac{180}{t}-15t-22.5=0

    Multiplying through by -t, we have 15t^2+22.5t-180=0

    Using the quadratic formula, t=\dfrac{-22.5\pm\sqrt{22.5^2-4\times15\times-180}}{2\times15}=\dfrac{-22.5\pm\sqrt{11306.25}}{30}

    Since t has to be positive, t=\dfrac{-22.5+106.3309}{30}\approx2.8 hours.

    Therefore, the time for going to fish is 2.8 hours and the time to return is 2.8 + 1.5 = 4.3 hours.

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