Aptitude Questions on Speed, Distance and Time

Ans: B

Let $x$ be the distance between A and B.

Haziel travels $x$ in 3 1/3 hours, so his speed is $x / (3 1/3) = 12$ miles/hour.

Ewa travels $x$ in 4 4/5 hours, so her speed is $x / (4 4/5) = 10$ miles/hour.

Therefore, Ewa’s speed is $\boxed{10}$ miles/hour.

Ans: B) 3 hours

Relative speed = 60 + 40 = 100 km/h.
Time taken = Distance / Relative speed = $\frac{300}{100} = 3$ hours.

Ans: A) 1 hour

Distance = Speed × Time = 5 × 4 = 20 km.
Time at new speed (7 km/h) = $\frac{20}{7} \approx ​2.86$ hours.
Time saved = 4 – 2.86 = 1.14 hours (approximately 1 hour and 8 minutes).

Ans: B) 36 km/h

Speed = Distance / Time = $\frac{150}{15} = 10$ m/s.
Converting to km/h: $10 \times 3.6 = 36$ km/h.

Ans: D) 24 km/h

Distance = Speed × Time = $18 \times \frac{40}{60} = 12$ km.
New speed = Distance / New time = $\frac{12}{\frac{30}{60}} = \frac{12}{0.5} = 24$ km/h.

Ans: A) 2 km/h

Downstream speed = $\frac{24}{2} = 12$ km/h, Upstream speed = $\frac{24}{3} = 8$ km/h.
Speed of the stream = $\frac{\text{Downstream speed} – \text{Upstream speed}}{2} = \frac{12 – 8}{2} = 2$ km/h.

Ans: C) 240 meters

Train speed = 54 km/h = 15 m/s.
Length of train = 15 × 18 = 270 meters.
Total distance to cross platform = 15 × 36 = 540 meters.
Length of platform = 540 – 270 = 270 meters.

Ans: C) 5 km/h

Downstream speed = $\frac{12}{2} = 6$ km/h, Upstream speed = $\frac{12}{3} = 4$ km/h.
Speed in still water = $\frac{\text{Downstream speed} + \text{Upstream speed}}{2} = \frac{6 + 4}{2} = 5$ km/h.

Ans: C) 150 m

Convert speed to m/s: $10 \times \frac{1000}{3600} = \frac{25}{9}$​ m/s.
Distance = Speed × Time = $\frac{25}{9} \times 54 = 150$ meters.

Ans: A) 4 seconds

Relative speed = 72 – 54 = 18 km/h = $18 \times \frac{5}{18} = 5$ m/s.
Total distance = 5 + 15 = 20 meters.
Time taken = $\frac{20}{5} = 4$ seconds.

Ans: C

1 km = 1000m and 1 h = 3600 s. So multiply the given speed by (1000/3600) to convert it into m/s

Ans: A

15 km = 1000m and 1 h = 3600 s. So multiply the given speed by (1000/3600) to convert it into m/s

Ans: A

Use the direct formula, Distance = Speed * Time

Ans: A

Use the direct formula, Distance = Speed * Time

Ans: D

Ans: B

Since the hoop has a radius of 12.5 inches, it has a circumference of:

2 x π x 12.5 = 25π = 25 x 3.14 = 78.5 inches

Since 1 foot is 12 inches, 75 feet is equivalent to 75 x 12 = 900 inches.

Thus, it will take 900/78.5 = 11.46 revolutions to roll the hoop 75 feet across the surface.

Since each revolution takes 10 seconds, 11.46 revolutions will take 114.6 seconds, or approximately 2 minutes.

Ans: D

Let the distance run be x miles and the distance walked be y miles.

We have, x + y = 8 …(i)

Also, time taken = 3 hours

Therefore, x/6 + y/2 = 3 …(ii)

Solving (i) for y, we get

y = 8 – x

Substituting this value of y in (ii), we get

x/6 + (8 – x)/2 = 3

⇒ x/6 + 4 – x/2 = 3

⇒ x/6 – x/2 = 3 – 4

⇒ (x – 3x)/6 = -1

⇒ -2x/6 = -1

⇒ -2x = -6

⇒ x = 3

Therefore, y = 8 – 3 = 5

Hence, the ratio of the distance walked to the distance traveled = y : (x + y)

= 5 : (3 + 5)

**= 5 : 8**

Ans: C

To solve this problem, let’s first understand Kendra’s current situation and the constraints she faces.

Kendra hikes at a constant rate of 12 minutes per kilometer. She has already hiked 2.75 kilometers east, which means she took:

$ 2.75 \text{ km} \times 12 \text{ minutes per km} = 33 \text{ minutes} $

Now, Kendra realizes she needs to return to the start and has 45 minutes to do so. Since she needs time to get back, we have to figure out how much further she can hike east before she must turn back.

When she turns back, she will retrace her path at the same rate. The total hiking time when going further east and then back to the start must equal 45 minutes. Since she has already spent 33 minutes hiking, she has:

$ 45 \text{ minutes} – 33 \text{ minutes} = 12 \text{ minutes} $

left to hike back towards the starting point.

**Determining maximum eastward distance before turning back:**

Since Kendra uses 12 minutes to cover 1 kilometer, in 12 minutes she will be able to cover:

$ \frac{12 \text{ minutes}}{12 \text{ minutes per km}} = 1 \text{ kilometer} $

Thus, she can continue hiking east for 0.5 kilometers before she would need to immediately turn around since it would take her 6 minutes to hike this extra 0.5 kilometers and another 6 minutes to get back to this point, totaling 12 minutes.

**Total distance hiked east before turning back:**

Adding this 0.5 kilometers to the initial 2.75 kilometers, she hiked a total distance of:

$ 2.75 \text{ km} + 0.5 \text{ km} = 3.25 \text{ kilometers} $

So, Kendra hiked a total of 3.25 kilometers east.