Question

Joseph needs to drive 42 miles. They were going to drive at a certain average speed, but if they drive 10 mph faster, the trip will take 6 minutes (1/10 of an hour) less time. How fast were they going to drive? Write out the equation(s) ​

Answers

  1. Answer:

    The speed is 60 mph.

    Step-by-step explanation:

    distance = 42 miles

    Let he drove with speed v and time is t.

    distance = speed x time

    42 = v t ….. (1)

    42 = (v + 10)(t – 1/10) ….. (2)

    42 = 42 -\frac{v}{10}+ 10 t - 1\\\\t =\frac{10+v}{100}\\\\Put in (1)\\\\42 = \frac{v(10+v)}{100}\\\\v^2 + 10 v - 4200 = 0 \\\\v = \frac{-10\pm \sqrt{100+4\times 4200}}{2}\\\\v =\frac{- 10 \pm 130}{2}\\\\v =- 70 mph, 60mph

    So, the speed cannot be negative so the speed is 60 mph.

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