320+ Time and Distance Problems With Solutions And Explanation

Q:

If a student walks at the rate of 4 mts/min from his home, he is 4 minutes late for school, if he walks at the rate of 6 mts/min he reaches half an hour earlier. How far is his school from his home ?

A) 100 mts	B) 96 mts
C) 98 mts	D) 120 mts

Answer & Explanation Answer: C) 98 mts

Explanation:

Let the distance between home and school is 'x'.
Let actual time to reach be 't'.
Thus, x/4 = t + 4 ---- (1)
and x/6 = t - 30 -----(2)
Solving equation (1) and (2)
=> x = 98 mts.

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Q:

A Bus is running at 9/10 of its own speed reached a place in 22 hours. How much time could be saved if the bus would run at its own speed ?

A) 1.5 hrs	B) 1.7 hrs
C) 2.2 hrs	D) 3.5 hrs

Answer & Explanation Answer: C) 2.2 hrs

Explanation:

Let the original Speed be "s" kmph
And the usual time be "t" hrs
Given that if the bus is running at 9s/10 kmph the time is 22 hrs
=> [9s/10] x 22 = t x s
=> 99/5 = t
=> t = 19.8 hrs

Hence, if bus runs at its own speed, the time saved = 22 - 19.8 = 2.2 hrs.

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Q:

A train travels 325 km in 3.5 hours and 470 km in 4 hours. Find the average speed of train ?

A) 107 kmph	B) 106 kmph
C) 72 kmph	D) 76 kmph

Answer & Explanation Answer: B) 106 kmph

Explanation:

As we know that Speed = Distance / Time
for average speed = Total Distance / Total Time Taken
Thus, Total Distance = 325 + 470 = 795 km
Thus, Total Speed = 7.5 hrs
Average Speed = 795/7.5 => 106 kmph.

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Q:

A jeep travels a certain distance taking 6 hrs in forward journey, during the return journey increased speed 12km/hr takes the times 4 hrs. What is the distance travelled by the jeep is ?

A) 244 km	B) 144 km
C) 444 km	D) 344 km

Answer & Explanation Answer: B) 144 km

Explanation:

Given a jeep travels a certain distance taking 6 hrs in forward journey
During the return journey, it takes 4 hrs with an increased speed 12 km/hr
Let 'x' be the distance.
Now, speed is given by distance/time.
Here the difference between both speeds = 12

$\frac{x}{4} - \frac{x}{6} = 12$

$\frac{3 x - 2 x}{12} = 12$

=> x = 144 km

Therefore, the distance travelled by the jeep in forward or return journey is x = 144 km.

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Q:

Joel travels the first 3 hours of his journey at 60 mph speed and the remaining 5 hours at 24 mph speed. What is the average speed of Joel's travel in kmph ?

A) 38 kmph	B) 40 kmph
C) 60 kmph	D) 54 kmph

Answer & Explanation Answer: C) 60 kmph

Explanation:

Average speed = Total distance / Total time.

Total distance traveled by Joel = Distance covered in the first 3 hours + Distance covered in the next 5 hours.

Distance covered in the first 3 hours = 3 x 60 = 180 miles
Distance covered in the next 5 hours = 5 x 24 = 120 miles

Therefore, total distance traveled = 180 + 120 = 300 miles.

Total time taken = 3 + 5 = 8 hours.

Average speed = 300/8 = 37.5 mph.

we know that 1 mile = 1.6 kms

=> 37.5 miles = 37.5 x 1.6 = 60 kms

Average speed in Kmph = 60 kmph.

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Q:

Karthik could cover a distance of 200 km in 22 days while resting for 2 hrs. per day. In how many days (approx) he will cover a distance of 250 km while resting for 2 hrs. per day and moving with 2/3rd of the previous speed ?

A) 41.25 days	B) 37.5 days
C) 39.75 days	D) 40 days

Answer & Explanation Answer: A) 41.25 days

Explanation:

Given Karthik can cover the distance of 200 kms resting 2 hrs per day in 22 days.

Let the initial speed be '1'

Hence, Time = 22(24hrs - 2)

Noe new speed = 2/3

Let the number of days he take be 'D'

Therefore, $\frac{22 (24 - 2) x 3}{200} = \frac{D (24 - 2) x 2}{250}$

D = 11 x 3 x 5/4 = 41.25 days. = 41 1/4 days.

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Q:

Three friends Rudra, Siva and Anvesh start to run around a circular stadium. They complete a revolution in 24, 36 and 30 seconds respectively. After how many minutes will they meet at the starting point ?

A) 60	B) 120
C) 360	D) 6

Answer & Explanation Answer: D) 6

Explanation:

For this we have to find the LCM of 24, 36 and 30

LCM of 24, 36 and 30 = 360 sec

360/60 min = 6 minutes.

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Q:

How many seconds will a 800 meter long train moving with a speed of 63 km/hr take to cross a man walking with a speed of 3 km/hr in the direction of the train ?

A) 48	B) 52
C) 38	D) 42

Answer & Explanation Answer: A) 48

Explanation:

Here distance d = 800 mts

speed s = 63 - 3 = 60 kmph = 60 x 5/18 m/s

time t = $\frac{800 x 18}{60 x 5}$ = 48 sec.

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