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Jamie recently drove to visit her parents who live 315 miles away. on her way there her average speed was 24 mph faster than on her way home. if Jamie spent a total of 9 hours driving find the two rates

Respuesta :

wizard123
Avg speed = miles/hours = 315/t

Let t1 be original time to drive there.  Let t2 be time to drive back.

t1 + t2 = 9   ------> t2 = 9 - t1

315/t1 = 315/t2 + 24

By substitution you have:

[tex]\frac{315}{t_1} = \frac{315}{9-t_1} + 24[/tex]

Eliminate fractions by multiplying by common denominator. (t)(9-t)
[tex]315(9-t_1) = 315 t_1 + 24 t_1 (9-t_1) \\ \\ 24t_1 ^2 - 846t_1+2835 = 0 \\ \\ 8t_1^2 - 282t_1 + 945 = 0[/tex]

Solve using quadratic formula (Note t1 < 9)
[tex]t_1 = \frac{15}{4} \\ \\ t_2 = 9-t_1 = \frac{36}{4} -\frac{15}{4} = \frac{21}{4}[/tex]

Finally, determine the two speeds.
[tex]\frac{315}{(15/4)} = 315*\frac{4}{15} = 84 \\ \\ \frac{315}{(21/4)} = 315*\frac{4}{21} = 60[/tex]

Final Answer:
Jamie traveled 84 mph on the way there and 60 mph on the way back.

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