Aptitude - Time and Distance - Discussion

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.

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.

1hr 40min 40sec = (60x60) + (40x60) + 48.
3600 + 2400 + 48.
6048.

Now converting into the min and then to hr.
6048/60 = 100.8 min.
100.8/60 = 1.68 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.

Friends why we multiply with 5/7. Please explain to me in detail.

5/7 of its actual speed, that's why.

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.

Time taken = 1hr 40min 48sec.
= 1hr 40*4/5 min =1 * 17/25hr = 17/25 hr.


Time = 42/25 hr ,
Actual speed = 5/7 * x,
distance=42.

s = d/t.
5/7 * x = 42 * 25/42
x = 25 * 7/5,
x = 35km/hr.