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A bus traveled from its depot to its destination at an average speed

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A bus traveled from its depot to its destination at an average speed of 60 kilometers per hour. On its return to the depot along the same route, the bus traveled at an average speed of only 40 kilometers per hour, making the trip 4 hours longer. What is the total distance of the round trip?

A. 360 kilometers
B. 400 kilometers
C. 600 kilometers
D. 800 kilometers
E. 960 kilometers

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[Reveal] Spoiler: OA

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Re: A bus traveled from its depot to its destination at an average speed [#permalink]

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Let time for first trip be x hrs

For first trip distance travelled = 60x
For round trip distance travelled 40(x+4) = 40x+160

60x = 40x + 160
x = 8 hrs.

Total Round trip distance = 60*8*2 = 960 kilometers

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Re: A bus traveled from its depot to its destination at an average speed [#permalink]

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Bunuel wrote:
A bus traveled from its depot to its destination at an average speed of 60 kilometers per hour. On its return to the depot along the same route, the bus traveled at an average speed of only 40 kilometers per hour, making the trip 4 hours longer. What is the total distance of the round trip?

A. 360 kilometers
B. 400 kilometers
C. 600 kilometers
D. 800 kilometers
E. 960 kilometers

Kudos for a correct solution.


The difference of speed (60-40 = 20 Kmph) is causing the delay of 4 hours

Distance = Speed x Time

Case 1: Distance = 60 x T While driving from Depot to Destination
Case 2: Distance = 40 x (T+4) While returning from Destination to Depot

Since the Distance Travelled is same in both cases therefore

60 x T = 40 x (T+4)
i.e. 20 T = 160
i.e. T = 8 Hours

i.e. (One side) Distance = 60 x T = 60 x 8 = 480
Total Distance of the round trip = 480 x 2 = 960 Km

Answer: Option E
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Let the distance be D km and T be time taken (in hours).

Now, D/60 = T; D/40 = T+4

D/60 - D/40 = -4
D(40-60/2400) = -4
D(-20/2400) = -4
D = 480 km

So, total distance = 960 km. Ans (E).
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Re: A bus traveled from its depot to its destination at an average speed [#permalink]

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Think about the concepts. The distance for the 2 trips is the same. So if RT = D, then R1T1 = R2T2.

You can now plug in the infromation:

60T = 40 (T + 4).

Solving T = 8


If the time for the first half took 8 hours and the speed was 60km/hour 8 x 60 = 480.


The total distance is then 480 + 480.
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Re: A bus traveled from its depot to its destination at an average speed [#permalink]

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New post 15 Jul 2015, 06:27
Bunuel wrote:
A bus traveled from its depot to its destination at an average speed of 60 kilometers per hour. On its return to the depot along the same route, the bus traveled at an average speed of only 40 kilometers per hour, making the trip 4 hours longer. What is the total distance of the round trip?

A. 360 kilometers
B. 400 kilometers
C. 600 kilometers
D. 800 kilometers
E. 960 kilometers

Kudos for a correct solution.


ALTERNATE METHOD

Speed reduces from 60 to 40 during return journey

i.e. New Speed while return (40) = (2/3)*60

But Distance = Speed x Time
But if Distance is multiplied with some factor (2/3 in this case) then Time should be multiplied with reciprocal of that factor (2/3 in this case)
i.e. Distance = (2/3)Speed x (3/2)Time


i.e. Time during return should be (3/2) of previous time
i.e. If Old Time = T
then, New Time during return = (3/2)T

and (3/2)T - T = 4 Hours
i.e. T = 8 Hours
i.e. (One side) Distance = 60x8 or 40x12 = 480
Both ways Distance = 480*2 = 960

Answer: Option E
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One way to think about this is that the Distance of the two trips is same. Thus, 40t + 4 hours = 60t. Further, since t will be the same on each side of the equation, you can subtract 40t from each side. That leaves you with 4 hours at 40kph, or 160 km = 20t, or t=8 hours. Finally, since the question asks for the distance of the roundtrip, you can find this by 60 x 8 x 2, or 960 km.
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Re: A bus traveled from its depot to its destination at an average speed [#permalink]

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Bunuel wrote:
A bus traveled from its depot to its destination at an average speed of 60 kilometers per hour. On its return to the depot along the same route, the bus traveled at an average speed of only 40 kilometers per hour, making the trip 4 hours longer. What is the total distance of the round trip?

A. 360 kilometers
B. 400 kilometers
C. 600 kilometers
D. 800 kilometers
E. 960 kilometers

Kudos for a correct solution.


Distance = Speed x Time

Trip 1: D = 60(x)
Trip 2: D = 40(x+40)

In round trip problems, the distances are the same.

60x=40(x+40)
60x=40x+160
20x=160
x=8

D = 60(8)
D=480
480(2) = 960 km round trip.
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Speed*time=distance
Let time for trip one be x
Trip1- d1= 60*x
Trip2- d2= 40*(x+4)
D1=D2
So x= 8
So d1= 480
d2= 480
Total distance =960 kms
E

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New post 17 Jul 2015, 03:29
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Bunuel wrote:
A bus traveled from its depot to its destination at an average speed of 60 kilometers per hour. On its return to the depot along the same route, the bus traveled at an average speed of only 40 kilometers per hour, making the trip 4 hours longer. What is the total distance of the round trip?

A. 360 kilometers
B. 400 kilometers
C. 600 kilometers
D. 800 kilometers
E. 960 kilometers

Kudos for a correct solution.


Time for bus to travel its route at average speed of 60kph: t
Given the information, we have equation: \(60t=40(t+4)\) --> \(t=8\)(hrs) --> total distance of the round trip \(=60*8*2=960\)(km)
Answer E

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Re: A bus traveled from its depot to its destination at an average speed [#permalink]

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New post 17 Jul 2015, 11:39
Bunuel wrote:
A bus traveled from its depot to its destination at an average speed of 60 kilometers per hour. On its return to the depot along the same route, the bus traveled at an average speed of only 40 kilometers per hour, making the trip 4 hours longer. What is the total distance of the round trip?

A. 360 kilometers
B. 400 kilometers
C. 600 kilometers
D. 800 kilometers
E. 960 kilometers

Kudos for a correct solution.


Let one way distance=d
Now, d/60+4=d/40
d/40-d/60=4
3d-2d/120=4
d=480
2d=960 km
Answer E

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Re: A bus traveled from its depot to its destination at an average speed [#permalink]

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New post 17 Jul 2015, 16:38
Bunuel wrote:
A bus traveled from its depot to its destination at an average speed of 60 kilometers per hour. On its return to the depot along the same route, the bus traveled at an average speed of only 40 kilometers per hour, making the trip 4 hours longer. What is the total distance of the round trip?

A. 360 kilometers
B. 400 kilometers
C. 600 kilometers
D. 800 kilometers
E. 960 kilometers

Kudos for a correct solution.


Two ways to solve this qn: (Maybe many ways)
1. Distance traveled is same in to and fro problems

60 * t = 40 * (t + 4) => Solving for t, t = 8

Distance = 8*60 = 480 (Usually this will be the trap answer). But they have asked for round trip distance. hence 2*D = 960.
Option E

2. Time Difference btw the two trips is 4 hours. This difference is bec of difference in speed.
Hence,
T2 - T1 =4
D/40 - D/60 = 4
Solving for D, D=> 480; 2D => 960.
Option E

Would like to know if there are any standard techniques that can be applied to all Time/Distance/Speed problems.
Thanks

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Re: A bus traveled from its depot to its destination at an average speed [#permalink]

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New post 19 Jul 2015, 13:04
Bunuel wrote:
A bus traveled from its depot to its destination at an average speed of 60 kilometers per hour. On its return to the depot along the same route, the bus traveled at an average speed of only 40 kilometers per hour, making the trip 4 hours longer. What is the total distance of the round trip?

A. 360 kilometers
B. 400 kilometers
C. 600 kilometers
D. 800 kilometers
E. 960 kilometers

Kudos for a correct solution.


800score Official Solution:

The distance formula is Distance = Rate × Time. To solve this question, set x as the length of time (in hours) for the first trip. The distance to the destination city is 60 × x, where rate = 60 and time = x. The return trip was 4 hours longer, so its distance is 40(x + 4).

Since we know the distances are the same, we can set them equal to each other and solve for x:
60x = 40(x + 4)
60x = 40x + 160
20x = 160
x = 8.

So, the trip took 8 hours, and its distance is 8 × 60 = 480 kilometers. The question asks for the roundtrip distance, so we double the length of the one-way trip: 480 × 2 = 960 kilometers.

The correct answer is choice (E).
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