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On the trip from Detroit to Columbus, Ohio, Mrs. Smith drove an average speed of 60 mph. Returning, her average speed was 55 mph. If it took her 1/3 of an hour longer on the return trip, how far is it from Detroit to Columbus?

Respuesta :

cerverusdante
Remember that Distance = (Average speed)(Time)
Let x be the distance between Detroit and Columbus. 
We know the journey from Detroit to Columbus  took a time t, and the returning trip took a time t+[tex] \frac{1}{3} [/tex]. We also know the Average speed of both journeys, so now we can set our equations:
[tex] \left \{ {{x=60t} \atop {x=55(t+ \frac{1}{3}) }} \right. [/tex]
Now, we can replace equation 1 into equation 2 to find t:
[tex]60t=55(t+ \frac{1}{3} )[/tex]
[tex]60t=55t+ \frac{55}{3} [/tex]
[tex]5t= \frac{55}{3} [/tex]
[tex]t= \frac{11}{3} [/tex]

Now that we know t, we can replace it into our equation 1 to get the distance:
[tex]x=(60)( \frac{11}{3} )[/tex]
[tex]x=220[/tex]

We can conclude that the distance between Detroit and Columbus is 220 miles. 

Answer:

220 miles

Step-by-step explanation:

Given :

Mrs. Smith drove an average speed of 60 mph.

Returning, her average speed was 55 mph.

It took her 1/3 of an hour longer on the return trip.

To Find : Distance between Detroit and Columbus

Solution :

Let the distance between Detroit and Columbus be x miles

She drove an average speed of 60 mph.

So, time taken by her to cover distance of x miles with speed of 60 mph

[tex]time =\frac{distance}{speed}[/tex]

[tex]time =\frac{x}{60}[/tex]

Thus , she took   [tex\frac{x}{60}[/tex]  hours while going from Detroit to Columbus .

While returning her speed was 55 mph.

So, time taken by her to cover the same distance but at a speed of 55 mph :

[tex]time =\frac{x}{55}[/tex]

Now we are given that she took 1/3 of hour more while returning .

So, [tex]\frac{x}{55} -\frac{x}{60} =\frac{1}{3}[/tex]

⇒ [tex]\frac{12x-11x}{660} =\frac{1}{3}[/tex]

⇒ [tex]\frac{x}{660} =\frac{1}{3}[/tex]

⇒ [tex]x=\frac{660}{3}[/tex]

⇒ [tex]x=220[/tex]

Hence ,  Detroit is 220 miles far from Columbus

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