Aptitude - Time and Distance - Discussion

Given:

Let actual speed be x.
Speed=(5/7)x
Time=1 hr 40 min 48 sec.
Now, lets convert time into hours as a whole.
48 sec=48/60 min = 0.8 min
->40+0.8=40.8 min
->40.8 min=40.8/60 hr
=0.68 hr.

->1 hr+0.68 hr=1.68 hr.
Now, we know that speed=distance/time.
(5/7)x=42/1.68.
x = (42/1.68)*(7/5),
= (4200/168)*(7/5),
= 35 km/hr.

1H 40M 48S.

First convert 48 sec to minutes min then 48/60 = 4/5.
Convert 40+4/5 nin to hours 51/75,
Then 1 51/75 = 126/75.

1 hour= 60 mins.
40 mins= 40/60 =0.6667hr.
48 sec = 48/60*60= 0.01333 hr.

1 hr 40 mins 48 sec = 1.68 hr.
42km/1.68 hr => 25kmph.
5/7 = 25kmph.

25 * 7/5 = 35kmph.

Is there any short cut trick to directly convert second min in hrs.

Time Taken=1 hr 40 min 48 sec = 3600+(40x60)+48 = 6048 sec
Distance = 42 km = (42x1000) = 42000 m
Let the Actual Speed be = x m/sec

(5/7)x*6048 = 42000
x = 175*7/126 m/sec
x = (175*7*18)/(126*5) km/hr.

= 35 km/hr (OPTION D)

Nice explanation @Soumava Bhattacharjee.

5/7 = 5\X*7/X = 35X.

1 Hr 40 Min 48 Sec => 1.68 Hr


Step by step explanation :
1 Hr = 60 Mins.

So,

1 Hr = 1 Hr
40 min = 40/60 hr = 2/3 hr.
1 Min = 60 Sec = 1/ 60 Hr.
1 Sec = 1/ 60 Min = 1/ 3600 Hr.

So,

48 Sec = 48/ 3600 Hr = 1/75 Hr
1 Hr 40 Min 48 Sec.
=> 1 + (2/3) + (1/75)
=> (75 + 50 + 1)/75
=> (126/75) Hr.
=> 1.8 Hr.

Convert km to m & hours to secs.
42km = 42000m.

1hr 40m 48s=1hr + 40mins + 38s.
(60*60) + (40*60) + 38.
6048s.

Let the speed be S.
5/7 S=42000/6048 m/s.
S=(42000*7)/(6048*5) m/s.
S=175/18 m/s.

Converting to kmph.
S=(175*18)/(18*5) kmph.
S=35 kmph.

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.