Antons family drove 216 miles to the lake averaging 48mi/hr. On the return trip home they averaged 54mi/hr. What was the total time that Antons family took driving to and from the Lake? A. 8hrs B. 8.5hrs C. 9hrs D. 9.5hrs

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Antons family drove 216 miles to the lake averaging 48mi/hr. On the return trip home they averaged 54mi/hr. What was the total time that Antons family took driving to and from the Lake? A. 8hrs B. 8.5hrs C. 9hrs D. 9.5hrs

Mathematics
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Each part of the trip is 216 miles. The first part is 216 miles at 48 mph. The second part is 216 miles at 54 mph. With speed questions, always start with the basic speed equation. Speed is the rate of distance per time. \(speed = \dfrac{distance}{time} \) Using s = speed, d = distance, and t = time, we can write: \(s = \dfrac{d}{t} \) Ok so far?
this is what i got for the going: 48 miles takes 1 hr 216 miles takes x hr x = 216*1/48 = 4.5 hr for the return: 54 miles takes 1 hr 216 miles take 216*1/54 = 4 hr so the total time is 9.5 hr

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Since the question is asking for a time, we take the basic speed equation, and we solve for time. \(s = \dfrac{d}{t} \) \(st = d\) \(t = \dfrac{d}{s} \) Now we have an equation for time. Time is distance divided buy average speed. With this equation, you can use the info of each half of the trip and find its time. then add the two times together.
First part: \(t = \dfrac{d}{s} = \dfrac{216~miles}{48 \frac{mi}{h}} = 4.5 ~h\) Second part: \(t = \dfrac{d}{s} = \dfrac{216~miles}{54 \frac{mi}{h}} = 4 ~h\) Total time = 4.5 h + 4 h = 9.5 h
Ok thanks you guys for all of your help @shadow13 @mathstudent55
You're welcome. Did you understand how to work the problem?

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