Sumit drove at the speed of 45 km/h from home to a resort, returning over the same route, he got stuck in traffic and took an hour longer. Also, he could drive only at the speed of 40 km/h. How many kilometers did he drive each way?

Let speed of train = 16k
Speed of car = 15k
Speed of bus = 480/8 = 60 km/h
According to the question,
16k = 60 x 4/3 = 80
? k = 5
? Speed of car = 15k = 15 x 5 = 75 km/h
? Required distance = Speed x Time
= 75 x 6 = 450 km

Let the constant speed = V
According to the question,
715/V - 715/(V + 10) = 2
? 1/V - 1/(V + 10) = 2/715
? [(V + 10) - V] / [V(V + 10)] = 2/715
? V² + 10V = 10 x 715/2
? V² + 10V - 3575 = 0
? V² + 65V - 55V - 3575 = 0
? V(V + 65) - 55(V + 65) = 0
? (V - 55) (V + 65) = 0
? V = 55 or V = - 65
Ignoring the negative value, we get V = 55
? Original speed of the motorcycle = 55 km/h

Speed of truck = Distance/time = 368/8 = 46 km/h
Now, speed of car = (speed of truck + 18) km/h = (46 + 18) = 64 km/h and
Distance travelled by car = 368 + 16 = 384 km
? Time taken by car = Distance/Speed = 384/64 h = 6 h

Relative speed of policeman with respect to thief = ( 11 - 10 ) = 1 km/h.
Now, relative distance covered by policeman in 6 min = Speed x Time
= (1 x 6)/60 = 1/10 km = 100 m
The distance between the policeman and thief after 6 min = (200 - 100) = 100 m

Let the required distance = L
According to the question,
L/(5/2) - L/(7/2) = 12/60 (difference between two times = 6 + 6 =12 min)
? 2L/5 - 2L/7 = 1/5
? 14L - 10L = 7
? 4L = 7
? L = 7/4 km

When serviced, the distance covered by the car = 65 x 5 = 325 km.
When not serviced, the time taken by the car to cover 325 km at 40 km/h
= 325/40 = 8.125 = 8 h (approx)

We know that speed is inversely proportional to time.
Therefore, Time taken by A : Time taken by B = 1/2 : 1/3

Let B takes T min. Then, A takes (T + 20) min.
? (T + 20) : T = 1/2 : 1/3 = 3 : 2
? (T + 20)/T = 3/2
? 2T + 40 = 3T
? T = 40
? A takes (T + 20) = (40 + 20) = 60 min.
? At double the speed, A would have covered it in 30 min.

Time taken to cover first 75 km = 75/25 = 3 h
Time taken to cover next 25 km = 25/5 = 5 h
Time taken to cover last 50 km of its journey = 50/25 = 2 h
Total distance = 75 + 25 + 50 = 150 km
Total time taken = 3 + 5 + 2 = 10 h
? Required average speed = Total distance / Total time taken
= 150/10 = 15 km/h

After sevicing speed of car = 60 km/h
? Distance covered in 6 h = 60 x 6 km = 360 km.
When not serviced, then time taken to cover 360 km = 360/50 = 7.2 h

Let they meet x km from A.
Then, according to the question,
x/40 = (1000 - x)/60
? 60 x = 40(1000 - x)
? 3x = 2000 - 2x
? 3x + 2x = 2000
? 5x = 2000 km
? x = 2000/5 = 400 km