Aptitude-on-speed-distance-time.pdf

Quantitative Aptitude: Speed Time & Distance
Dr. Manjunatha. P
manjup.jnnce@gmail.com
Professor & Dean Academics
JNNCE Shimoga
Dept. of ECE
J.N.N. College of Engineering, Shimoga
Distance
Speed
Distance=Speed X Time
Time
October 18, 2022

Relationship between Distance, Speed and Time
Distance
Speed
Distance=Speed X Time
Time
Distance = Speed × Time
Speed =
Distance
Time
Time =
Distance
Speed
Dr. Manjunatha. P (JNNCE) Quantitative Aptitude: Speed Time & Distance October 18, 2022 2 / 17

Formula to convert Km/hr to m/s
1 hour = 60 × 60 = 3600 seconds
1 km = 1000 meters
x km/hr = x
1000
3600
= x
10
36
= x
5
18
m/s
Formula to convert m/s to Km/hr
1 second =
1
60 × 60
=
1
3600
hour
1 meter =
1
1000
km
x m/s = x
1/1000
1/3600
= x
3600
1000
= x
36
10
= x
18
5
km/hr

Average Speed
Average Speed =
Total distance traveled
Total time taken
=
d1 + d2 + d3 + . . . + dn
t1 + t2 + t3 + . . . + tn
When the distance is constant: Average speed
Average Speed =
2xy
x + y
Where, x and y are the two speeds at which the same distance is covered.
When the time taken is constant: Average speed =
Average Speed =
x + y
2
Where, x and y are the two speeds at object traveled for the same time.

Q1. A truck traveling at a speed of 40mph takes 4 hours to cover a distance.
What should be its speed to cover the same distance in 2 hours?
Solution:
Distance = speed × Time
= 40 × 4 = 160miles
speed =
Distance
Time
=
160
2
= 80 mph

Q2. A car travels at a speed of 40 km/hr for 2 hours and then decides to slow
down to 30 km/hr for the next 2 hours. What is the average speed?
Solution:
Distance traveled in 2 hours is
Distance D1 = Speed × Time = 40km/hr × 2hours = 80km
Distance traveled in another 2 hours is
Total Distance traveled is
DistanceD = D1 + D2 = 80 + 60 = 140 Km
Average speed is
Savg =
Total Distance traveled
Total Time taken
=
140
4
= 35 Km/hr

Q3. A train travels at a speed of 100 km/hr for 2 hours and then slows down
to 120 km/hr for the next 3 hours. What is the average speed of the train?
Solution:
Total Distance traveled is
DistanceD = D1 + D2 = 200 + 360 = 560 km
Average speed is
Savg =
Total Distance traveled
Total Time taken
=
560
5
= 112 Km/hr

Q4. A bus travels for the first 4 hours at a speed of 90 kmph, and the
remaining distance in 6 hours at speed of 50 kmph. What is the average speed
of the bus?
Solution:
Distance covered in 4 hours= 90 × 4 = 360 km
Distance covered in 6 hours= 50 × 6 = 300 km
Total distance = 360 + 300 = 660 km
Total time = 4 + 6 = 10 hours
Average speed =
660
10
= 66 kmph

Q5. A train travels from A to B at a speed of 20 km/hr and returns at a
speed of 60 km/hr. What is the average speed of the train?
Solution:
x = 20 km/hr
y = 60 km/hr
Average speed is
Savg =
2xy
x + y
=
2 × 20 × 60
20 + 60
=
2400
80
= 30 Km/hr

Q6. A man goes from A to B at a speed of 20 kmph and comes back to A at
a speed of 30 kmph. Find his average speed for the entire journey?
Solution:
x = 20 km/hr
y = 30 km/hr
Average speed is
Savg =
2xy
x + y
=
2 × 20 × 30
20 + 30
=
1200
50
= 24 Km/hr

Q7. Raju hikes up a hill at 4 mph and comes down at 6 mph. If the total time
taken for the total journey is 3 hours, what was the distance between the
hilltop and the foothills?
Solution:
x = 4 mph, x = 6 mph
Average speed is
Savg =
2xy
x + y
=
2 × 6 × 4
6 + 4
= 4.8 mph
Distance traveled is
Distance = Time × speed = 3 × 4.8 = 14.4
Hence, the one-way distance = 7.2 miles.

Q8. A bus travels from A to B at a speed of 80 kmph and returns from B to
A through the same route at 60 kmph. What was the average speed during
the two way journey?
Solution:
Average speed when the distance is same
Average speed =
2xy
x + y
=
2 × 80 × 60
80 + 60
=
9600
140
= 64

Q9. Find the average speed of train that covers a certain distance by running
at 72 kmph for first 2 hours and 80 kmph for next 2 hours
Solution:
When time is equal
Average speed =
x + y
2
=
72 + 80
2
= 76 kmph
Alternate method
Total distance covered is
Total distance = 72 × 2 + 80 × 2
= 304 km
Average speed =
304
(2 + 2)
= 76 kmph

Q10. A bus travels from A to B at a speed of 40 kmph, returns from B to A
at speed of 30 kmph and again goes from A to B at a speed of 60 kmph.
What is the average speed of the bus?
Solution:
Average speed when the distance is same
Total distance = d + d + d = 3d
Total time =
d
40
+
d
30
+
d
60
=
3d + 4d + 2d
120
=
9d
120
Average speed =
3d
9d
120
=
3d × 120
9d
= 40 kmph

Q11. If a person walks at 12 km/hr instead of 9 km/hr, he would have walked
18 km more. What is the actual distance traveled by him?
Solution:
Let x km is travelled with a speed of 9
km/hr
He travelled x + 18 km with a speed of
12 km/hr
Time =
Distance
speed
=
x
9
Time =
Distance
speed
=
x + 18
12
Equate the above equations
x
9
=
x + 18
12
12
9
=
x + 18
x
= 1 +
18
x
18
x
=
4
3
− 1 =
1
3
x = 18 × 3 = 54 km
Therefore the actual distance is 54km.

Q12. A farmer traveled a distance of 53 km in 8 hours. He traveled partly on
foot at 4 km/hr and partly on bicycle at 10 km/hr. What is the distance
traveled on foot?
Solution:
Let distance traveled on foot is x km
Distance travelled on bicycle is 53 − x km
Time =
Distance
speed
8 =
x
4
+
53 − x
10
8 =
10x + 212 − 4x
40
=
6x + 212
40
320 = 6x + 212
6x = 320 − 212 = 108
x =
108
6
= 18 km

Q13. Two trains A and B start simultaneously in the opposite direction from
two points P and Q and arrive at their destinations 16 and 9 hours
respectively after their meeting each other. At what speed does the second
train B travel if the first train travels at 120 km/h
Solution:
S1 = 120 kmph, S2 =? t1 = 16 hours t2 = 9 hours
S1
S2
=
r
t2
t1
120
S2
=
r
9
16
=
3
4
S2 =
4
3
× 120 = 160 kmph

Thank You

Aptitude-on-speed-distance-time.pdf

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