Time and Distance – Questions and detailed solutions

Question 21. A train covers a distance of 500 km in 6 hours. If it travels at a speed of 100 kmph for the first 2 hours and then reduces its speed by 10%, what will be its average speed for the entire journey?

• (a)73.10 km/h.
• (b)77.20 km/h.
• (c)88.35 km/h.
• (d) 93.33 km/h.

Answer

(d) 93.33 km/h.
To calculate the average speed for the entire journey, we need to consider the total distance traveled and the total time taken.
The train covers a distance of 500 km in 6 hours.
First, let’s calculate the distance covered in the first 2 hours at a speed of 100 km/h:
Distance = Speed × Time
Distance = 100 km/h × 2 hours
Distance = 200 km
Next, let’s calculate the distance covered in the remaining time, which is 6 hours – 2 hours = 4 hours.
To find the reduced speed after decreasing it by 10%, we subtract 10% of the initial speed from the initial speed:
Reduced Speed = Initial Speed – (Initial Speed × 10%)
Reduced Speed = 100 km/h – (100 km/h × 0.10)
Reduced Speed = 100 km/h – 10 km/h
Reduced Speed = 90 km/h
To calculate the distance covered in the remaining 4 hours at a reduced speed of 90 km/h:
Distance = Speed × Time
Distance = 90 km/h × 4 hours
Distance = 360 km
Now, we can calculate the total distance covered:
Total Distance = Distance in first 2 hours + Distance in remaining 4 hours
Total Distance = 200 km + 360 km
Total Distance = 560 km
To calculate the average speed, we divide the total distance by the total time:
Average Speed = Total Distance / Total Time
Average Speed = 560 km / 6 hours
Average Speed ≈ 93.33 km/h (rounded to two decimal places)
Therefore, the average speed for the entire journey is approximately 93.33 km/h.

Question 22. . A car travels at a speed of 90 kmph for the first 6 hours and then reduces its speed by 20%. How far will it travel in the next 3 hours?

• (a) 216 km.
• (b)312 km.
• (c)310 km.
• (d)311 km.

Answer

(a) 216 km
To calculate the distance the car will travel in the next 3 hours, we first need to find the distance it covered in the initial 6 hours.
Distance = Speed × Time
Distance = 90 km/h × 6 hours
Distance = 540 km
Next, let’s calculate the reduced speed after decreasing it by 20%.
Reduced Speed = Initial Speed – (Initial Speed × 20%)
Reduced Speed = 90 km/h – (90 km/h × 0.20)
Reduced Speed = 90 km/h – 18 km/h
Reduced Speed = 72 km/h
Now, we can calculate the distance traveled in the next 3 hours using the reduced speed:
Distance = Speed × Time
Distance = 72 km/h × 3 hours
Distance = 216 km
Therefore, the car will travel a distance of 216 km in the next 3 hours.

Question 23. A man walks at a speed of 4 kmph for the first half of his journey and then increases his speed by 15% for the second half. If he covers a total distance of 15 km, how long does he take to complete the journey?

• (a)4.5 hours
• (b) 3.5 hours
• (c)5.5 hours
• (d)2.5 hours

Answer

(b) 3.5 hours
To find the time it takes for the man to complete the journey, we need to calculate the time taken for each half of the journey and then sum them together.
Let’s start by finding the distance covered in the first half of the journey. Since the total distance is 15 km, the first half would be half of that, which is 15 km / 2 = 7.5 km.
To calculate the time taken for the first half of the journey, we use the formula:
Time = Distance / Speed
Time = 7.5 km / 4 km/h = 1.875 hours
Next, let’s calculate the distance covered in the second half of the journey, which is also 7.5 km.
To find the increased speed for the second half, we need to add 15% to the original speed of 4 km/h:
Increased Speed = 4 km/h + (4 km/h × 15%)
Increased Speed = 4 km/h + (0.6 km/h) = 4.6 km/h
To calculate the time taken for the second half of the journey, we use the formula:
Time = Distance / Speed
Time = 7.5 km / 4.6 km/h ≈ 1.63 hours
Finally, to find the total time taken to complete the journey, we add the times for the first and second halves:
Total Time = Time for First Half + Time for Second Half
Total Time = 1.875 hours + 1.63 hours = 3.505 hours (rounded to three decimal places)
Therefore, the man takes approximately 3.5 hours to complete the entire journey.

Question 24. A train covers a distance of 200 km in 2 hours. If the speed of the train is increased by 30%, how long will it take to cover the same distance?

• (a)2.44 hours
• (b) 1.54 hours
• (c)3.45 hours
• (d)4.45 hours

Answer

(b) 1.54 hours
To calculate the new time it will take for the train to cover the same distance with a 30% increase in speed, we first need to find the original speed of the train.
Let’s denote the original speed of the train as “s” and the time taken to cover the distance as “t.”
The train covers the distance of 200 km in 2 hours, so we have:
Distance = Speed × Time
200 km = s × 2
Now, let’s consider the scenario where the speed of the train is increased by 30%. The new speed would be:
New Speed = Original Speed + (Original Speed × 30%)
New Speed = s + (s × 0.30) = s + 0.30s = 1.30s
To calculate the new time, we can rearrange the formula:
Time = Distance / Speed
Time = 200 km / (1.30s)
Now, we need to substitute the original speed in terms of “s” back into the equation.
200 km = s × 2
s = 200 km / 2 = 100 km/h
Substituting this value back into the new time equation:
Time = 200 km / (1.30 × 100 km/h)
Time = 200 km / 130 km/h
Time ≈ 1.54 hours (rounded to two decimal places)
Therefore, it will take the train approximately 1.54 hours to cover the same distance with the increased speed of 30%.

Question 25. A car covers a distance of 150 km in 2.5 hours. If the car stops for 20 minutes every hour, what is its average speed in km per hour?

• (a)37.10 km/h.
• (b)27.20 km/h.
• (c)57.10 km/h.
• (d) 47.30 km/h.

Answer

(d) 47.30 km/h.
To calculate the average speed of the car, we need to consider the total distance traveled and the total time taken, including the time spent during the stops.
The car covers a distance of 150 km in 2.5 hours.
Now, we need to account for the time spent during the stops. The car stops for 20 minutes every hour, so for a total of 2.5 hours, there are 2 stops, each lasting for 20 minutes.
Total time spent in stops = 2 stops × 20 minutes/stop = 40 minutes
To convert the 40 minutes into hours, we divide by 60 minutes/hour:
Total time spent in stops = 40 minutes / 60 minutes/hour = 0.67 hours
Now, we can calculate the total time taken for the journey, including the time spent in stops:
Total time = Travel time + Time spent in stops
Total time = 2.5 hours + 0.67 hours = 3.17 hours
Therefore, the car’s average speed is calculated as:
Average speed = Total distance / Total time
Average speed = 150 km / 3.17 hours
Average speed ≈ 47.30 km/h (rounded to two decimal places)
Therefore, the car’s average speed is approximately 47.30 km/h.