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

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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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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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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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.

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

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

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

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

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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