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Solved Examples(Set 1) - Time and Distance

1. A man takes $5$ hours $45$ min in walking to a certain place and riding back. He would have gained $2$ hours by riding both ways. The time he would take to walk both ways is
A. $8$ hrs $45$ minB. $11$ hrs
C. $7$ hrs $45$ minD. $9$ hrs $20$ min
Discuss
answer with explanation

Answer: Option C

Explanation:

Solution 1

Given that time taken for riding both ways will be $2$ hours lesser than the time needed for waking one way and riding back.

Therefore,
time needed for riding one way = time needed for waking one way - $2$ hours

Given that time taken in walking one way and riding back $=5$ hours $45$ min

Hence, the time he would take to walk both ways
$=5$ hours $45$ min + $2$ hours
$=7$ hours $45$ min

Solution 2

Let the distance be $x$ km. Then,

Time taken to walk $x$ km + Time taken to ride $x$ km
$=5$ hour $45$ min $=5\dfrac{45}{60}$ hour
$=5\dfrac{3}{4}$ hour $=\dfrac{23}{4}$ hour $\cdots(1)$

Time taken to ride $2x$ km
$=5$ hour $45$ min $-2$ hour
$=3$ hour $45$ min $=3\dfrac{45}{60}$ hour
$=3\dfrac{3}{4}$ hour $=\dfrac{15}{4}$ hour $\cdots(2)$

Solving $(1)$ and $(2)$

$(1)×2 \implies$
Time taken to walk $2x$ km + Time taken to ride $2x$ km $=\dfrac{23}{2}$ hour $\cdots(3)$

$(3)-(2)\implies$
Time taken to walk $2x$ km
$=\left(\dfrac{23}{2}-\dfrac{15}{4}\right)=\left(\dfrac{46}{4}-\dfrac{15}{4}\right)$
$=\dfrac{31}{4}=7\dfrac{3}{4}$ hours $=7$ hours $45$ minutes
2. A person crosses a $600$ metre long street in $5$ minutes. What is his speed in km per hour?
A. $8.2$B. $7.2$
C. $4.2$D. $6.1$
Discuss
answer with explanation

Answer: Option B

Explanation:

Solution 1

Distance $=600$ metre $=0.6$ km
Time $=5$ minutes $=\dfrac{1}{12}$ hour

$\text{Speed}=\dfrac{\text{distance}}{\text{time}}=\dfrac{0.6}{\left(\dfrac{1}{12}\right)}$ $=7.2\text{ km/hr}$

Solution 2

Distance $=600$ metre
Time $=5$ minutes $=5×60$ seconds $=300$ seconds

$\text{Speed}=\dfrac{\text{distance}}{\text{time}}=\dfrac{600}{300}=2\text{ m/s}\\=2×\dfrac{18}{5}\text{ km/hr}=\dfrac{36}{5}\text{ km/hr}$ $=7.2\text{ km/hr}$
3. Excluding stoppages, the speed of a bus is $54$ kmph and including stoppages, it is $45$ kmph. For how many minutes does the bus stop per hour?
A. $11$B. $12$
C. $10$D. $9$
Discuss
answer with explanation

Answer: Option C

Explanation:

Speed of the bus excluding stoppages $=54$ kmph
Speed of the bus including stoppages $=45$ kmph

Loss in speed when including stoppages $=54-45=9\text{ kmph}$
$\Rightarrow$ In $1$ hour, bus covers $9$ km less due to stoppages.

Hence, time in which the bus stops per hour
= Time taken to cover $9$ km
$=\dfrac{\text{distance}}{\text{speed}}= \dfrac{9}{54}\text{ hour}=\dfrac{1}{6}\text{ hour }$ $=\dfrac{60}{6}\text{ min}=10\text{ min}$
4. A man complete a journey in $10$ hours. He travels first half of the journey at the rate of $21$ km/hr and second half at the rate of $24$ km/hr. Find the total journey in km.
A. $112$ kmB. $121$ km
C. $242$ kmD. $224$ km
Discuss
answer with explanation

Answer: Option D

Explanation:

Solution 1

reference: formula 4

Average Speed $=\dfrac{2×21×24}{21+24}=22.4\text{ km/hr}$

Total distance $=22.4×10=224\text{ km}$

Solution 2

distance = speed × time

Let time taken to travel the first half $=x$ hr
Then, time taken to travel the second half $=(10-x)$ hr

Distance covered in the first half $=21x$
Distance covered in the second half $=24(10-x)$

But distance covered in the first half = Distance covered in the second half
$\Rightarrow 21x=24(10-x)\\\Rightarrow 21x=240-24x\\\Rightarrow 45x=240\\\Rightarrow 9x=48\\\Rightarrow 3x=16\\\Rightarrow x=\dfrac{16}{3}$Hence, distance covered in the first half
$=21x=21×\dfrac{16}{3}=7×16=112\text{ km}$

Total distance $=2×112=224\text{ km}$
5. A car traveling with $5/7$ of its actual speed covers $42$ km in $1$ hr $40$ min $48$ sec. What is the actual speed of the car?
A. $30$ km/hrB. $25$ km/hr
C. $40$ km/hrD. $35$ km/hr
Discuss
answer with explanation

Answer: Option D

Explanation:

time $=1$ hr $40$ min $48$ sec
$=1$ hr $+\dfrac{40}{60}$ hr $+\dfrac{48}{3600}$ hr
$=1+\dfrac{2}{3}+\dfrac{1}{75}=\dfrac{126}{75}\text{hr}$

distance $=42$ km

$\text{speed}=\dfrac{\text{distance}}{\text{time}}=\dfrac{42}{\left(\dfrac{126}{75}\right)}$ $=\dfrac{42×75}{126}=25\text{ km/hr}$
$\Rightarrow \dfrac{5}{7}$ of the actual speed $=25$
$\Rightarrow$ Actual speed $=25×\dfrac{7}{5}=35\text{ km/hr}$

Comments(94)

profileNiveda
2015-07-08 16:37:16 
The speed of a bus increases by 4 km after every 2 hours. If the distance travelling in the first 2 hour was 70 km. what was the total distance travelled in 24 hours?
like 1 dislike 0 reply
profileMegha
2015-07-15 05:45:39 
Since the speed increases every 2 hrs, in 24 hrs the speed increases 12 times.
Arithmetic Progression
Sum of n terms=n/2*(2a+(n-1)d)
=12/2*(2*70+(11*4))
=1104
like 1 dislike 0
profileVishal Jaiswal
2015-04-09 06:35:46 
Give the HCF of two no.is 16.find the LCM if their product is 19712.
like 0 dislike 0 reply
profileDev
2015-04-09 18:40:46 
Product of two numbers = Product of their HCF and LCM
19712 = 16 * LCM
LCM = 19712/16 = 1232
like 0 dislike 0
profilevarthini
2015-04-06 14:21:29 
Walking at a rate of 4 km an hour, a man covers a distance in 3 hours. Running at a speed of 8 km, he will cover the same distance in

a)5 hrs 45 min
b) 9 hrs 60 min
c)11 hrs 90 min
d) 1 hr 30 min
like 0 dislike 0 reply
profileJay
2017-01-09 17:23:04 
First of all , there is a correction in your question. It will be 8 km/hr.
Now, Distance = speed*velocity.
Hence total distance = 12 km. Now, Time = Distance / Velocity , which gives 12/8= 1.5 hours , which is 1 hour and 30 mins. :D
like 0 dislike 0
profileShubham gupta
2015-11-07 08:35:59 
Total distance covers= 4×3=12km

At running @8km/hr the time taken
= 12/8 = 1hr 30 min
like 0 dislike 0
profileDev
2015-04-08 19:54:36 
speed = 4 km/hr
time = 3hrs
distance = speed * time = 12 km

New speed = 8 km
required time = distance/speed = 12/8 = 3/2 = 1.5 hour = 1 hr 30 minute

or more easily
4 km/hr  : 3 hrs
8 km/hr : 1.5 hrs (as speed is inversely proportional to time when distance is constant)
like 0 dislike 0
profilejunaid
2015-04-04 15:08:21 
if a cyclist had gone 3km/hr faster , he would have taken 1 hour and 20 min less to ride 80 kms. what time did he take
like 0 dislike 0 reply
profileDev
2015-04-08 19:21:18 
Let his normal speed = x km/hr
distance = 80 km

Normal time he takes = 80/x hr
If he had gone 3km/hr faster, time taken = 80/(x+3) hr
Savings of time = 1 hr 20 min = 1 1/3 hr = 4/3 hr

80/x  - 80/(x+3) = 4/3
1/x  - 1/(x+3) = 1/60
60(x+3) - 60x = x(x+3)
180 = x^2 + 3x
x^2 + 3x - 180 = 0
(x+15)(x-12)=0
x = 12 (taking +ve value)

Required time = distance/speed = 80/12 = 20/3 hrs
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