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Manager  Joined: 14 Apr 2014
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A car traveled from Los Angeles to San Francisco in 6 hours at an aver  [#permalink]

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Question Stats: 78% (02:07) correct 22% (02:23) wrong based on 237 sessions

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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. (6 + 6x/y)*60
B. (6 + 6y/x)*60
C. 30(x + y)
D. 10(x + y)
E. (x + y)/360

Originally posted by ajaym28 on 02 Nov 2014, 22:15.
Last edited by Bunuel on 14 Aug 2017, 03:55, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: A car traveled from Los Angeles to San Francisco in 6 hours at an aver  [#permalink]

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Ashishmathew01081987 wrote:
ajaym28 wrote:
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?

Not Sure about the ans pls help !

There is something missing in the question. Are you sure that you didn't miss some part of the question ???

As per the above given data you can arrive at an equation :

Let,

Total distance from LA to SF = D miles

While travelling from LA to SF,
Distance = D Miles, Speed = X miles/hr, Time = 6 hours

D = 6X ; ----------------------------------------------[Dist = Time*Speed]

While Travelling from SF to LA,

Distance = D Miles, Speed = Y miles/hr.

Now total distance traveled for round trip = 2D ---------------------- (A)

Average Speed for round trip = 2*X*Y / (X+Y) -----------------------(B)

Therefore,
Total Time = Total Dist / Average Speed

T = 2D* (X+Y) / 2*X*Y ------------------------------- From (A) & (B)

T = D*(X+Y) / XY

T= 6X*(X+Y) / XY ------------------------------------- {Substituting D=6X}

T=6(X+Y) / Y

Converting 6hours into minutes we get 6*60 = 360 Minutes

Therefore,
T=360 (X+Y) / Y

If you have OA's then substitute in above equation to get the answer.
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Re: A car traveled from Los Angeles to San Francisco in 6 hours at an aver  [#permalink]

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I did it in a little simpler way LA TO SF at x miles per hour for 6 hours. So distance= 6X

Now, SF to LA at Y miles per hour. Hence, time for SF to LA = 6X/Y

We already know time for LA to SF i.e. 6 hours. Hence total time = 6X/Y + 6 Hours or 6(X+Y)/Y hours or 360 (X+Y)/Y minutes
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Re: A car traveled from Los Angeles to San Francisco in 6 hours at an aver  [#permalink]

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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?

1. (6 + 6x/y) * 60
2. (6 + 6y/x) * 60
3. 30 (x+y)
4. 10 (x+y)
5. (x+y) / 360

Can someone 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 roundtrip = 12x. The rates (in minutes) are x/60 for the 1st leg, and y/60 for the 2nd leg.

Thus isn't the time simply the total distance over the combined rates? Or 12x / [ (x+y) / 60] --> 720x / (x+y)?

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Re: A car traveled from Los Angeles to San Francisco in 6 hours at an aver  [#permalink]

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v0latility

The total Time is = Time taken to Travel from Los Angeles to San Francisco + Time taken to Travel from San Francisco to Los Angeles

Time taken to Travel from Los Angeles to San Francisco = This is already given as 6 hrs

Time taken to Travel from San Francisco to Los Angeles
=> We know the distance between San Francisco to Los Angeles is 6x, as the route taken during return journey is same.
=> We know the average rate during the return journey is y miles per hour

therefore, Time taken to Travel from San Francisco to Los Angeles = 6x/y

Total Time = 6 + 6x/y hr
Total Time in mins = (6 + 6x/y) * 60

hope this helps
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Re: A car traveled from Los Angeles to San Francisco in 6 hours at an aver  [#permalink]

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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?

total trip time in hours=6+6x/y➡6(x+y)/y
total trip time in minutes=360(x+y)/y
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Re: A car traveled from Los Angeles to San Francisco in 6 hours at an aver  [#permalink]

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Quote:
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) (6 + 6x/y) * 60
B) (6 + 6y/x) * 60
C) 30 (x+y)
D) 10 (x+y)
E) (x+y) / 360

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

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Re: A car traveled from Los Angeles to San Francisco in 6 hours at an aver  [#permalink]

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ajaym28 wrote:
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?

OA
360 (X+Y) / Y

The goal is to find the time in minutes for the round-trip from LA to San Francisco.

Let x = 40 and y = 20.

In this case, then the total distance is 6*40 = 240 miles.

The time for the return is 6+240/20 = 6 + 12 = 18 hours.

18*60 = 1080 is the target number we want.

(A) matches this target value.
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Re: A car traveled from Los Angeles to San Francisco in 6 hours at an aver  [#permalink]

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ajaym28 wrote:
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. (6 + 6x/y)*60
B. (6 + 6y/x)*60
C. 30(x + y)
D. 10(x + y)
E. (x + y)/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)

Cheers,
Brent
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Re: A car traveled from Los Angeles to San Francisco in 6 hours at an aver  [#permalink]

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ajaym28 wrote:
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. (6 + 6x/y)*60
B. (6 + 6y/x)*60
C. 30(x + y)
D. 10(x + y)
E. (x + y)/360

Let x =2 miles/hr

Distance = 6 * 2 = 12 miles

Let y = 3 miles/hr

Time of return = 12/3 = 4 hrs

Total time = 10 hrs = 600 minute

When you scan C, D & E, you will find it very small..........Eliminate

Check choice A

(6 + 6x/y)*60 = (6 + 6 * 2/3)*60 = 600...........Keep

(6 + 6x/y)*60 = (6 + 6 * 3/2)*60......Certainly it will be larger as multiply 6 * 1.5...No need to calculate.....Eliminate

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Re: A car traveled from Los Angeles to San Francisco in 6 hours at an aver  [#permalink]

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ajaym28 wrote:
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. (6 + 6x/y)*60
B. (6 + 6y/x)*60
C. 30(x + y)
D. 10(x + y)
E. (x + y)/360

It's an easy problem. Here also we use the only formula that we have for time and distance.
Avg speed = tot distance /tot time taken.

From Eq--1 we can find the distance of the route.

Distance D = Avg speed * time taken
= 6*x
= 6X

In eq-2 we can find time for return journey

Time = distance / speed
= 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 + 6X/Y
= (6 + 6X/Y)60 minutes

Posted from my mobile device
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