Aptitude - Time and Distance - Discussion

First total distance is 61km and time is 9 hour.
S=d/t, s= 61/9=6.7~6.8.

Then apply this formula for different speeds;
2xy/X+y = 6.8,
72/13 = 6.8,
72=13 * 6.8,
72-88.4 = 16.4~16.

X/4 is km ph.

(61-x)/9 is also kmph.
When these are added it should give kmph.
Why only 9 is thereafter =, why not 61/9?

Please, anyone clear my doubt.

Total distance D = 61
4km/hr for 4 hr = 16
9km/hr for 5 hr = 45
Adding 45+16=61.

Hence answer =16.

By Using alligation method.

4:5=9.
So, 4 * 4 = 16 by walking,
5*9 = 45 by cycle.

@All.

Here's my explanation.

Basically, I deduced the given information into two equations:

df = 4tf -----> (1) [ Distance = Speed x Time (Speed mentioned)]
db = 9 x (9 - tb) --->(2) (Same as above)
Where,
df = distance on foot,
tf = time taken on foot,
db = distance on a bicycle,
tb = distance on bicycle

Now, db = 61 - df, as df + db = 61 (given),
Also, tb = 9 - tf, as tf + tb = 9 (given),

So now keeping values together we get,
df = 4tf-->from (1)
61 - df = -5tf + 81 -->from (2)

Solving these two equations, we get the value of tf which comes out to be 4 hours and hence putting this value in (1) we get, df = 16km!

Hi, its simple,

Total distance = 61 km.
Time taken = 9 hr.

Speed by foot = 4 km/hr.
Speed by bicycle = 9 km/hr.

So split the total hours into 2 parts like 4 hr + 5 hr = 9 hrs.
Multiply it with the speed by foot and bicycle like.

4 hr*4 km/hr = 16 km.
5 hr*9 km/hr = 45 km.

Add 16 + 45 = 61 km (total distance covered).
They asked distance covered by foot. So answer is 16. :).

How can 5x=80? just explain it.

Can anybody explain this problem please.

Partly means is it not (x/2 )/4+(x/2)/9=9 if d is taken as the total distance?

Please tell me.

No. 14 can also be solved simultaneously using a system of linear equations:

Let the time on foot = x, at 4kph, the distance on foot would be 4x.
Let the time on the bicycle = y, at 9kph, the distance travelled on the bicycle would be 9y.
It is given that:
x + y = 9, (Eqt. 1); and,
4x + 9y = 61 (Eqt. 2)
To solve for y;
x = 9 - y.
4(9 - y) + 9y = 61.
36 - 4y + 9y = 61.
36 + 5y = 61.
5y = 61 - 36.
5y = 25.
y = 5.

Substitute 5 for y in Eq. 2, then solve.
4x + 9(5) = 61
4x + 45 = 61
4x = 61 - 45
4x = 16
The distance travelled on foot is 16 kilometres.