M4maths Previous Puzzles

28 Aug 2013 walk

A man walks up a mountain at the rate of 2 km an hour and down by a way 6 km longer at the rate of 7/2 km an hour. He is out eight hours altogether. How far has he walked?

OPtion

1) 43 km
2) 38 km
3) 32 km
4) 29 km
5) 26 km
6) 22 km
7) 20 km
8) 19 km
9) 17 km
10) None of these

Solution

Let the way up be x km
Time taken to climb up = x/2 hours.
The way down = (x+6)km
Time taken to climb down =(x+6)/(7/2)= 2(x+6)/7
Therefore the total time of the journey = (x/2)+{2(x+6)/7}=8
solve x = 8
Total distance = x+x+6 = 22km.
option 6

Correct Option: 6 Best Solution (33)

Vinay Sipani    11 years AGO

Let time taken to walk up the mountain = Tu
Let time taken to travel down the mountain = Td
=> T1 + T2 = 8 hrs
Let distance up the mountain = D kms
=> Distance travelled down the mountain= (D+6) kms

=> Tu = D/2 ,
=> Td = (D+6)/(7/2) = (2D + 12) / 7

=> [ D/2 ] + [(2D + 12) / 7 ] = 8
=> 7D + 4D + 24 = 112
=> D = 8 kms

=> Total distance travelled = D + D + 6 = 22 kms

Like? Yes (12) | No (4)  

Md Shahnawaz Shahab   11 years AGO

let the distance traveled by the man uphill be 'x' km, therefore the distance traveled by him downhill will be (x+6) km.
Now, adding the time taken by both the journeys we get,

x/2 + 2(x+6)/7 = 8

solving for x, we get x = 8 km
therefore total distance traveled by the man will be x + (x+6) = 8+8+6 = 22km.

Like? Yes (6) | No (3)  

KUNAL GAURAV   11 years AGO

Let the distance covered while climbing up the mountain be d.
So the distance covered while coming downwards will me d+6.

Time taken during whole journey = d/2 + (d+6)2/7
Since, total time of the journey is given as 8 hrs
So,
On solving we get d = 8
So total distance covered will be = 8+8+6 = 22

Like? Yes (4) | No (1)  

mohini gupta   11 years AGO

let initialdistance be x
hence,x/2+(x+6)/3.5=8
by solving
x=8
total distance=8+8+6=22

Like? Yes (4) | No (2)  

ShAg   11 years AGO

for upward journey:
distance = x
speed = 2kmph
time = x/2
for downward journey:
distance = x+6
speed = (7/2)kmph
time = (x+6)/(7/2) = (2x+12)/7

total time = 8hrs.
hence (x/2) + ((2x+12)/7) = 8
=> x = 8

hence total distance = x + (x+6) = 22km

Like? Yes (1) | No   

Abhijeet Kumar   11 years AGO

let
x be the distance to walk up at 2 km/h
& (x+6) be the distance to walk down at 7/2=3.5 km/h.

(x/2)+(x+6)/3.5 = 8
after solving this equation x=8 & x+6=14
so, the total walking distance = (x)+(x+6) = 22.

Like? Yes (3) | No (2)  

priyanka kumari   11 years AGO

x/2+(x+6)*2/7=8
x=8
total distance=8+(8+6)=22

Like? Yes (1) | No   

sanjay kumar saha   11 years AGO

x is upward distance

x/2+(x+6)*2/7=8
x=8
total dis=8+(8+6)=22

Like? Yes (2) | No (1)  

richa ahuja   11 years AGO

let distance covered by him up the mountain is x km
therefore distance covered by him down the mountain is x+6 km
distance =speed*time
time=distance/speed
total time=8 hours
x/2+2(x+6)/7=8
on solving this
x=8
total distance=x+x+6=8+8+6=22km

Like? Yes (2) | No (1)  

Alok Kumar   11 years AGO

let time is t hr
2t - 7/2*(8-t) = 6
so t = 4
and 2t + 7/2*(8-t) = 22 km

Like? Yes (2) | No (2)  

Kumar Ankit   11 years AGO

Suppose total distance to walks up a mountain be xkm and down the mountain be (x+6)km.
Time taken to walks up a mountain be x/2 hr(Since given speed to walks up a mountain be 2km/hr).

Time taken to walks down a mountain be 2(x+6)/7 hr(Since given speed to walks down a mountain be 7/2km/hr).

Hence,total time taken=x/2+2(x+6)/7=8
on solving this we get x=8
Hence total distance cover is x+(x+6) i.e
8+(8+6)=22

Like? Yes (2) | No (2)  

rahul jha   11 years AGO

going UP @ 2km/hr
so cover distance:8km need
time:4hr
going down @ 7/2km/hr
6km longer so need to cover 14 km distance..
so required time=(2*14)/7=4 hr
so,total time=8hr
distance=22 KM

Like? Yes (3) | No (3)  

Avinash Kumar   11 years AGO

let the distance covered by the man while going up be as 'x'
so distance covered while coming down will be 'x+6'
So the equation will be
x/2 + 2x+12/7 =8
solving this we get x=8
so total distance covered by the man is x+x+6
or 8+8+6
or 22

Like? Yes (1) | No (1)  

Alok kumar   11 years AGO

let he walks up s distance
so, s=2*t1
now he walks down (s+6)
so, (s+6)=7/2*t2
now t1+t2=8 (given)
solving these eqtns we will get s=8(upward distance)
so, downward distance=(s+6)=14
so,total distance= (8+14)=22

Like? Yes (1) | No (1)  

SATYAM SAURABH   11 years AGO

from above qus:
8 =d/2 + (d+6)/3.5)
d=8
total walking distance 8+8+6=22

Like? Yes (1) | No (1)  

Jacky shevkani   11 years AGO

let t1 and t2 be the time taken when the men walls up and walls down the mountain respectively.

let x km be the distance covered while going up and (x+6) km be the distance covered while coming down the mountain.

therefore
t1=(x/2)
t2=(x+6)/(7/2)

adding both the above equations we get
t1+t2=(x/2)+((x+6)/(7/2))

since total time taken is 8hours
therefore
t1+t2=8

substituting in above we equation and solving it we he
x=8km
and
x+6=14km
therefore total distance covered is 8+14=22km

Like? Yes (1) | No (1)  

Jasmine Khan   11 years AGO

assume that he travelled for xkm while going up and while coming back he has travelled (x+6)km
let us denote as,
d1=x,d2=x+6,s1=2km/hr ands2=7/2km/hr
d1/s1+d2/s2=8
x/2+2(x+6)/7=8
7x+4x+24=8*14
11x=112-24
11x=88
x=8
he has travelled for 8+(8+6)=22km

Like? Yes (1) | No (1)  

Madhu pericherla   11 years AGO

d=xkm,s=2kmph,t1
d=x+6,s=7/2,t2
given
T=t1+t2=8hrs
speed=distance/time
time=distance/speed
8hrs=(x/2)+((x+6)/(7/2))
while solving we will get x=8
total journey=x+(x+6)=8+8+6=22km
(so ans is 22km)

Like? Yes (1) | No (1)  

Devendra Marghade   11 years AGO

If up distance=x & down distance=x+6
[(x/2)+((x+6)2/7)]=8,solving x=8
Total distance walked=x+(x+6)=8+14=22 km

Like? Yes (1) | No (1)  

T Lokesh   11 years AGO

let the distance covered by him while going up =x
then time t1 =x/2
distance covered by him while coming down =x+6
time t2 =(x+6)/(7/2)
total time =8
x/2 + (2x+12)/7 =8
so x=8
so total distance = 8+8+6 =22

Like? Yes (1) | No (1)  

sivaraman   11 years AGO

consider x is distance
The mountain up time is x/2km/hr
The mountain down time is (x+6)/ 7/2kh/hr
so

x/2 = (x+6)/(7/2)
x/2= 2(x+6)/7
x/2=(2x+12)/7

do cross multiply

7x=2(2x+12)
7x=4x+24
7x-4x=24
3x=24
x=8

so up time is 8, down time is 8+6=14
add up and down time is =8+14
22km

Like? Yes (1) | No (1)  

ravi chandra singh   11 years AGO

t1=1hr
t2=6*2/7=12/7
t=t1+t2=19/7
required distance=19/7*(2+6)=21.71=22km

Like? Yes (1) | No (1)  

Parthiban C   11 years AGO

(x/2)+((x+6)2)/7=8
then x=8
finally ans =8+8+6=22

Like? Yes (1) | No (1)  

Chandni Maurya   11 years AGO

ans=(6). 22km
let x is the distance to walk up the mountain and t1 is the corresponding time,
t2 is the return time.
we know,
distance=velocity*time
according to question,
x=2*t1 ---(1)
x+6=(7/2)*t2 ----(2)
(2)-(1)
-2*t1 + (7/2)*t2 =6 ----(3)
t1+t2 = 8 (given) -----(4)
solving 3 and 4
t1=t2 = 4 hr => x= 8 km
total distance= x+x+6 = 8+8+6 = 22 km

Like? Yes (1) | No (1)  

IFFAT IRAM   11 years AGO

let the distance for the forward journey be x km
distance for backward journey=(x+6) km
time for forward journey=x/2 hr
time taken for backward journey=2(x+6)/7 hr
x/2 + 2(x+6)/7 = 8
(7x+ 4(x+6))/14 = 8
11x + 24 = 8*14
11x=112-24
11x=88
x=8 km
he has walked 8+(8+6)=22km

Like? Yes (1) | No (1)  

mohamed ismail   11 years AGO

let x be distance travelled ,y be. time taken

according to the condition, the eqns will be
2x+7y equal to 44
2y-x equal to 0
solving we get. 22 kms

Like? Yes (1) | No (1)  

sudipta sadhukhan   11 years AGO

LET, THE DISTANCE HE COVERED AT THE TIME OF CLIMBING UP IS D KM.
THE DISTANCE HE COVERED AT THE TIME OF CLIMBING DOWN IS (D+6) KM.
NOW,
ACCORDING TO THE QUESTION,
D/2+((D+6)/3.5)=8
=>D=8
SO HE COVERED A TOTAL DISTANCE OF 8+(8+6)=22 KM.☻

Like? Yes (1) | No (1)  

Bingumalla Abinay   11 years AGO

x=2t
x+6=3.5(8-t)
t=4

so total distance = 2t+3.5t=8+14=22

Like? Yes (1) | No (2)  

Rats   11 years AGO

time to go up(t1)=x/21
time to go down(t2)=((x+6)2)/7
t1+t2=8
On solving all these eq. we get
x=8
So total distance=x+(x+6)=8+14=22

Like? Yes (1) | No (2)  

gaurav   11 years AGO

x/2 + 2(x+6)/7 = 8
on solving we get x= 8
so total distance = 8+8+6 = 22

Like? Yes (1) | No (2)  

Pankaj   11 years AGO

up=2km/hr
d=3.5km/hr
av=2.75
dis=2.75*8=22 ANS.

Like? Yes (2) | No (3)  

Akshay Hanswal   11 years AGO

x/2 +(x+6)/(7/2)=8
On solving we get x=8 so total walk=8+8+6 i.e. 22km

Like? Yes (1) | No (2)  

rahul   11 years AGO

8 km walks up in 4 hr at 2km/h nd 14 km walks down in hr at speed of 7/2 km/h

Like? Yes (1) | No (2)