Aptitude - Time and Distance - Discussion

1 hr 40 min 48 sec lets assume 48 sec as one minute then total 1 hr 41 min that means 101 min now convert 101 min to hr = 101/60 = 1.683. This is just for those who find it difficult to convert.

1st convert 48 sec to min. 48/60 = 0.8 again convert 0.8 min to hr 0.8/60 = 0.0133 i.e 48sec = 0.0133 hr.
Now convert 40 min to hr 40/60 = 0.6666,
40 min = 0.666 hr,
Now 1 hr 40 min 48 sec = 1 + 0.666 + 0.01333 = 1.6793 = 1.68 hr,

Given:
Speed = 5/7 of its actuall speed = 0.71428 of its actual speed,
Distance D = 42 km,
Time T = 1.68 hr,

Formula S = D/T,
0.71428 * actuall speed = 42/1.68,
0.71428 * actuall speed = 25,
Actuall speed = 25/0.71428,
Actuall speed = 35 km/hr.

Here, in the time conversion- we have 1 hr 40 min 48s right!

First, convert seconds to mins - 48/60 which gives -4/5 min.

So, till this step we got, 1hr 40 (4/5) min.

Next, we need to convert 40 (4/5) minutes INTO hours - [40 (4/5) ]/60 (like previous conversion of 48sec to mins we convert 40 (4/5) min INTO hours by dividing with 60.

HEere, [40 (4/5) ]/60 we reciprocate (denominator 60/1) by [40 (4/5) * 1/60].

Which gives, [ (5*40) +4]/5 *1/60 (here, we changed the mixed fraction 40 (4/5) into an improper fraction).

Which gives, [ (200+4) /5 * (1/60) ] -> [204/5 * 1/60] =204/300 = 51/75.

THEREFORE, TIME IN HOURS= 1(51/75) HR.

Let the actual speed be x.

In the question they said that the car speed is 5/7 times the actual speed,so it becomes 5/7(x).

Now we have, distance : 42km.
Speed : 5/7 (x).
Time : 1hr 40min 48sec(we can convert this whole 1hr 40 min 48 secs to seconds then divide it by 60 * 60..

Now convert the time into seconds...1hr + 40min = 60min + 40min 100min=6000secs,6000secs + 48 secs = 6048 secs).

Therefore , time : 6048/3600 = 126/75.
Now, The equation is 42 = 5/7 (x) * 126/75.

John starts at a specific time from home to his son's school and reach there at 4pm at the time his son's school ends. But one day the school ended up at 3pm and the boy started walking towards the home without waiting for his father. His david as regularly went to pick him up and they both met on the road and reached home 20 mins before the regular reaching time at home. So for who much time did the son walked from school towards his home.

Formula for speed:

Speed = distance/ time.

Let speed is x. Now we have;
Speed = 5/7x.
Distance = 42km.

Time = 1 hour 40 minutes 48 second.
For making unit equal.

Time = 1hrs + 40/60hrs + 48/60 * 60hrs.
= 100/60 +48/60*60.
= 504/300 hrs,
= 126/75 hrs,
= 42/25hrs.

Now put all the values in formula.
5/7x =42/42/25.
5/7x = 1050/42.
5/7x = 25.
x = 25*7/5.
=175/5
= 35kmph.
So, the Correct answer is D.

By using formula S = D/T.

S=(5/7)x is the actual speed.
(5/7)x = 42/{1+(40÷60)+(48÷3600)} by using DST
(5/7)x = 42/{1+(2÷3)+(1÷75)} by dividing terms we got;
(5/7)x = 42/{1+[(150+3)÷225]},
(5/7)x = 42/{[225+153]÷225},
(5/7)x = (42 * 225)÷(225+153),
(5/7)x = (9420)÷(378),
x = (9420÷378)*(7/5).

By cancelling terms we got;
X = 1890 ÷ 54.

By dividing we got;

X = 35kmph.

Yes, as we all know that SPEED=DISTANCE/TIME.

Here they gave in hours so we have to convert entire to hours then we got 126/75 as time
And let us assume actual speed = x.
5/7 of speed = 5x/7.
Distance = 42,
By applying in the formula
Speed =distance/time.
5x/7 = 42/126/75,
5x/7 = 75 * 42/126 ,
Then we go 5x/7 = 3150/126.
While Criss cross we got,
630x = 22050,
X = 35km/hr.

1hr 40min 48sec = 1hr +(40)min +(48/60)min
= 1hr +(40)min +(4/5)min [as,(4/5)=(8/10)=0.8]
= 1hr +(40.8)min
= 1hr +(40.8/60)hr [as,(40.8/60)=(68/100)]
= 1hr +(0.68)hr
= 1.68hr

According to question,

(5/7)x * 1.68 = 42 (where, x- actual speed)
Solving this we get, x = 35km/hr(actual speed)

Actual distance covered by car is 42 km in 1 hr 40 min 48 sec = 100.8 minutes. Now just divide total km by total minutes took = 42/100.8 = 0.416667 km per minute.

Then per hr speed = 0.416667 km per minute * 60 minutes = 25 kmph as the car was running @ 5/7 of it's actual speed.
Then 5 = 25 and 7 = ?
The answer is 25/5 = 5.
5 * 7 = 35 kmph.

Another method:

Let the original speed be x.
5/7 of the speed = 5x/7.

48 seconds = 48/3600 hours = 1/75 hours.
40 minutes = 40/60 =2/3 hours.
1 hour.

So total time in hours = 1+2/3 +1/75.

75+50+1 / 75=126/75 hours.

speed = distance / time.
speed = 42 / 126/75.
speed= 42*75/126.

5x/7= 25.

5x=25*7.

x= 25*7/5.

x=35.

x= 35 km/h.