Question

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?

Answer 1

220 miles

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

`time =(distance)/(speed)`

`time =(x)/(60)`

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 :

`time =(x)/(55)`

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

So,
`(x)/(55) -(x)/(60) =(1)/(3)`

⇒
`(12x-11x)/(660) =(1)/(3)`

⇒
`(x)/(660) =(1)/(3)`

⇒
`x=(660)/(3)`

⇒
`x=220`

Hence , Detroit is 220 miles far from Columbus

Answer 2

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+
`(1)/(3)`. We also know the Average speed of both journeys, so now we can set our equations:

`\left \{ {{x=60t} \atop {x=55(t+ (1)/(3)) }} \right.`
Now, we can replace equation 1 into equation 2 to find t:

`60t=55(t+ (1)/(3) )`

`60t=55t+ (55)/(3)`

`5t= (55)/(3)`

`t= (11)/(3)`

Now that we know t, we can replace it into our equation 1 to get the distance:

`x=(60)( (11)/(3) )`

`x=220`

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