A car traveled from Los Angeles to San Francisco in 6 hours

[BTGmoderatorLU]

A car traveled from Los Angeles to San Francisco in 6 hours at an average rate of x miles per hour. If the car returned along the same route at an average rate of y miles per hour, how long did it take for the car to make the entire round trip, in minutes?

$$A.\ \left(6+\frac{6x}{y}\right)\cdot60$$
$$B.\ \left(6+\frac{6y}{x}\right)\cdot60$$
$$C.\ 30\cdot\left(x+y\right)$$
$$D.\ 10\cdot\left(x+y\right)$$
$$E.\ \frac{\left(x+y\right)}{360}$$

The OA is A.

Can any expert please explain to me what I'm doing wrong:

I know that the car traveled 6x one way, so it must travel back 6x the other way, so total round trip 12x. Te rates (in minutes) are x/60 for the first leg, and y/60 for the second leg.

Thus, isn't the time simply the total distance over the combined rates? Or
$$\frac{12x}{\frac{\left(x+y\right)}{60}}\ \Rightarrow \frac{720}{\left(x+y\right)}?$$
Thanks in advance.

[Brent@GMATPrepNow]

A car traveled from Los Angeles to San Francisco in 6 hours at an average rate of x miles per hour. If the car returned along the same route at an average rate of y miles per hour, how long did it take for the car to make the entire round trip, in minutes?

$$A.\ \left(6+\frac{6x}{y}\right)\cdot60$$
$$B.\ \left(6+\frac{6y}{x}\right)\cdot60$$
$$C.\ 30\cdot\left(x+y\right)$$
$$D.\ 10\cdot\left(x+y\right)$$
$$E.\ \frac{\left(x+y\right)}{360}$$

A car traveled from Los Angeles to San Francisco in 6 hours at an average rate of x miles per hour.
Distance = (time)(rate)
So, distance from Los Angeles to San Francisco = (6)(x) = 6x miles

The car returned along the same route at an average rate of y miles per hour
We know the distance = 6x miles
Time = (distance)/(rate)
So, time spent driving from San Francisco to Los Angeles = 6x/y hours

TOTAL TIME = (time driving Los Angeles to San Francisco) + (time driving San Francisco to Los Angeles)
= 6 hours + 6x/y hours
= (6 + 6x/y) HOURS

How long did it take for the car to make the entire round trip, in MINUTES?
To convert HOURS to MINUTE, we multiply the number of hours by 60
So, time (in minutes) = (6 + 6x/y)(60)

Answer: A