Aptitude - Time and Distance - Discussion

@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 penna, the problem is so simple..let me explain

Given that

Distance travelled by farmer =61 km in 9 hours

let the farmer travelled x distance by foot @ 4 km/hr

Therefore he travelled 61-x distance by bicycle @ 9 km/hr

already we know formula to find time, time = distance /speed

Time taken by the farmer = time taken on foot + taken by bicycle
9 = x/4 + 61-x/9

solving we can get x value.

We assumed that x is the distance covered by foot.

So that is the answer.

61km travel in 9hours.

4kmph by foot --> taken time is "x"
9kmph by bicycle --> taken time is "y"
So,

x + y = 9 ---> (1)
Distances = speed × time.
Distance by foot--> 4 × x = 4x.
Distance by bicycle--> 9 × y = 9y.
So,
4x + 9y = 61 ----> (2)

If we solve (1) & (2) equations, we can got.
y = 5
x = 4.

So;
Distance by foot = 4x,
=4 × 4.
=16km.

Equation 1 : DF= 4 * t1.
Equation 2 : DB= 9 * (9-t1). As distance= speed * time.

Here let t1 be time taken by foot.
Here time taken by bicycle is (total time taken - time taken by foot).

Now equate the equation;
Now DF+DB= 4t1 + 9 * (9-t1).
Now we know DF+DB is 61.
61= 4t1+81-9t1.
61=-5t1+81.
-20=-5t1.
t1=4.

So, the Time taken by foot is 4hrs.
Now distance by foot = speed * time.
D = 4 * 4 = 16 km.

Logically, if he travels x km by feet then reaming distance should be in multiples of 9 since he had travelled remaining distance with 9kmph.

Let we try from options:

A. 14 remaining distance=61-14=47 which is not multiple of 9 since get cancelled.
B. 15 remaining distance= 61-15=46 also not multiple of 9 so cancelled.
C. 16 remaining distance=61-16=45 it's multiple of 9 so we get the answer.

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. :).

From options it will be simple to solve;

61-14 = 47,
61-15 = 46,
61-16 (Dist travelled by foot) = 45, Only this is divisible by 9.

So the answer is 16.

Note: This is applicable here only because the hours are given in terms of Integers, not in fraction.
And the answer will only be the multiple of 4.

Please someone helps me, they have asked only for bare foot then why are we considering the bicycle also?

v = d/t:
we know the time for the full trip (i.e) 9 hours.
He walks bare foot at speed of 4kmph;
why can't we just multiply and find the answer?
d = v * t;
d = 9 * 4.
d = 36km.

It's very easy.

Farmer travels - 4km/hr.
Speed = 4km/hr and Time = 4 hours.

HOW?
- Well in 1 hour he travels 1 Km, then in 4 hours he will travel 4km.

So, Distance = Speed * Time.
= 4km/hr * 4hr.
= 16km (Hr gets cancel).

Hey Friends,

If Answer for PARTLY travelled is 16. Ok.

Means 4 km/ hr for foot he walked 16km.

And 9 km/hr for bicycle did 45 km ok.

Than 5 km/hr=45 means 9 km hr.

Now 4km/hr=16 means 4 km/hr.

So how it becomes partly ? Partly means 4:30 hr am I right. ?