Aptitude - Time and Distance - Discussion

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.

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.

To convert the time 1 hr 40 min 48 sec to hours,

Hours = 1 + (40 ÷ 60) + (48 ÷ 3600),
Hours = 1 + 0.67 + 0.0134.
Hours = 1.68 hrs, which is nothing but 126/75.