A car traveled from Los Angeles to San Francisco in \(6\) hours at an average rate of \(x\) miles per hour. If the car

[Vincen]

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. \(\left(6 + \dfrac{6x}{y}\right)\cdot 60\)
B. \(\left(6 +\dfrac{6y}{x}\right)\cdot 60\)
C. \(30(x + y)\)
D. \(10(x + y)\)
E. \(\dfrac{x + y}{360}\)

Answer: A

Source: Manhattan GMAT

[swerve]

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. \(\left(6 + \dfrac{6x}{y}\right)\cdot 60\)
B. \(\left(6 +\dfrac{6y}{x}\right)\cdot 60\)
C. \(30(x + y)\)
D. \(10(x + y)\)
E. \(\dfrac{x + y}{360}\)

Answer: A

Source: Manhattan GMAT

Here also we use the only formula that we have for time and distance.
\(\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}\)

From the Equation 1 we can find the distance of the route.

\(\text{Distance} = \text{Speed}\cdot \text{Time}\)
\(= 6\cdot x\)
\(= 6x\)

In equation 2 we can find time for return journey

\(\text{Time} = \dfrac{\text{Distance}}{\text{Speed}}\)
\(= \dfrac{6x}{y}\)

Now we have 2 times. We add them to get time for round trip and multiply with \(60\) to convert into minutes.

Total time \(= 6 + \dfrac{6x}{y}\)
\(= \left(6 + \dfrac{6x}{y}\right)\cdot 60\) minutes \(\Longrightarrow\)A

[Scott@TargetTestPrep]

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. \(\left(6 + \dfrac{6x}{y}\right)\cdot 60\)
B. \(\left(6 +\dfrac{6y}{x}\right)\cdot 60\)
C. \(30(x + y)\)
D. \(10(x + y)\)
E. \(\dfrac{x + y}{360}\)

Answer: A

Solution:

Since distance = rate x time and we are given that the car traveled from Los Angeles (LA) to San Francisco (SF) in 6 hours at an average rate of x miles per hour, we can express the distance from LA to SF as 6x. We are also given that the car returned along the same route (i.e., traveling the same distance) from SF to LA at an average rate of y miles per hour. If we let t = the time returning from SF to LA, in hours, we have:

6x = yt

t = 6x/y hours = time from SF to LA

Thus, the round trip time = time from LA to SF + time from SF to LA = 6 + 6x/y hours

Finally, we convert our time from number of hours to number of minutes by multiplying the number of hours by 60, since 1 hour = 60 minutes:

(6 + 6x/y) hours = 60(6 + 6x/y) minutes

Answer: A