## Journey with stoppage

`=("Difference between speeds"/"Speed without stoppage") xx 60 min`

### Concept review questions

50 km covered without stoppage in 60 minutes. Speed with stoppage = 30 kmph

`-> 30 km` covered with stoppage in 60 minutes. 50 km covered in effective time of 60 minutes.

`:.` 30 km is covered in `(60/50 ) xx 30 = 36min`, that is with stoppage the car is travelled in an effective time of 36 minutes per hour.

Hence the time for rest = `60 min - 36 min = 24 min`

**Alternate Method I:**

Speed without stoppage `= 50 kmph`

Speed with stoppage `= 30 kmph`

Time spent for stoppage `= ((50 - 30)/50) xx 60 = 24 min`

**Alternate Method II:**

Speed without stoppage `= 50 kmph `

Speed with stoppage `= 30 kmph`

Decrease in speed `= ((50 - 30)/50) xx 100 = 40%`

Therefore stoppage `= 40%` of time

`= 40%` of 60 mins

`= 24 min`

Stoppage time `= 30 min/hr = 1/2` of an hr

I.e. the variation happened in the return speed `= 1/2` of the initial speed `= 1/2 P kmph`

Average Speed `= (2 xx P xx 1/2P)/(P + 1/2P)`

`-> 2/3P = 40 kmph`

`P = 60kmph`; ie: Speed from A to B `= 60kmph`

## Speed of moving bodies as per the speed of sound (Report of Guns- problem)

It is an old pattern of questions from time and distance. Initial period of GMAT exam GMAC (the counsel which conduct GMAT exam) started to ask it is in a 700+ range bin of questions, even though the concept is very simple.

### Concept:

Two guns were fired from same place at an interval of 'x' minutes. If a person who is approaching the shooting place by train/ car and hears the shooting sound at an interval of 'y' minutes, then it is possible to find the speed of the train/car.

Speed of the sound in air is `330 "m/s"` in a fixed value.

Distance covered by the train in y minutes = Distance covered by the sound in (x-y) minutes

`= 330 xx (x-y) xx 60` minutes

Speed of the train `= (330 xx (x-y) xx 60)/y = (330 xx 60 xx (x - y))/1000 xx 60/y = 1188[(x-y)/y] ` kmph

### Concept review questions

In 30 seconds sound covers the same distance as Mr.Kennedy covers in 13 mins 30 sec `330xx30 = 9900 m = 9.9 km`

Distance covered by Kennedy in 13.30 mins `= 9.9 km`

Speed of Mr.Kennedy `= 90 xx (60/13.5) = 44km` (13 min 30 sec = 13.5 min)

**Alternate Method:**

As per the above discussed rule, speed of Kennedy `= 1188[(14 - 27/2)/13.5] = 44km`

Speed of train `= 1188[(8 - 36/5)/(36/5)] = 132 km`

Interval of shots `= 8 min`

Distance covered `= 132 xx (8/60) = 17.6km`