Time and Distance – Questions and detailed solutions

Question 6.A boat can cover a certain distance downstream in 5 hours. If the speed of the boat is doubled, how long will it take to cover the same distance downstream?

• (a)1.4 hours
• (b)2.75 hours
• (c) 2.5 hours
• (d)3.5 hours

Answer

(c) 2.5 hours
To calculate the time it will take for the boat to cover the same distance downstream when its speed is doubled, we first need to determine the original speed.
Let’s denote the original speed of the boat as “s” and the time taken to cover the distance downstream as “t.”
Distance = Speed × Time
Since the boat covers a certain distance downstream in 5 hours, we have:
Distance = s × 5
Now, let’s consider the scenario where the speed of the boat is doubled. The new speed would be 2s.
To calculate the new time, we can use the formula:
Time = Distance / Speed
Time = (s × 5) / (2s)
Time = 5 / 2
Time = 2.5 hours
Therefore, when the speed of the boat is doubled, it will take 2.5 hours to cover the same distance downstream.

Question 7.A train covers a distance of 480 km in 6 hours. If it travels at a speed of 80 kmph for the first 3 hours and then reduces its speed by 20%, what will be its average speed for the entire journey?

• (a)70.25 km/h.
• (b) 71.11 km/h.
• (c) 72.55 km/h.
• (d) 73.55 km/h.

Answer

(b) 71.11 km/h
To find the average speed for the entire journey, we need to consider the total distance traveled and the total time taken.
The train travels at a speed of 80 km/h for the first 3 hours, covering a distance of 80 km/h × 3 hours = 240 km.
For the remaining 480 km – 240 km = 240 km, the train reduces its speed by 20%.
The new speed after the reduction is 80 km/h – (20% of 80 km/h) = 80 km/h – (0.2 × 80 km/h) = 80 km/h – 16 km/h = 64 km/h.
To calculate the time taken to cover the remaining distance of 240 km at a speed of 64 km/h, we use the formula:
Time = Distance / Speed
Time = 240 km / 64 km/h = 3.75 hours.
Now, we can calculate the total time taken for the entire journey:
Total Time = Time for the first leg + Time for the second leg
Total Time = 3 hours + 3.75 hours = 6.75 hours.
The total distance covered is 480 km.
Average Speed = Total Distance / Total Time
Average Speed = 480 km / 6.75 hours ≈ 71.11 km/h (rounded to two decimal places).
Therefore, the average speed for the entire journey is approximately 71.11 km/h.

Question 8. A car travels at a speed of 72 kmph for the first 4 hours and then reduces its speed by 25%. How far will it travel in the next 2 hours?

• (a) 98 km
• (b) 80 km
• (c) 110 km
• (d) 108 km

Answer

(d) 108 km
To calculate the distance the car will travel in the next 2 hours, we first need to find the distance it covered in the initial 4 hours.
Distance = Speed × Time
Distance = 72 km/h × 4 hours
Distance = 288 km
Next, let’s calculate the reduced speed after decreasing it by 25%.
Reduced Speed = Initial Speed – (Initial Speed × 25%)
Reduced Speed = 72 km/h – (72 km/h × 0.25)
Reduced Speed = 72 km/h – 18 km/h
Reduced Speed = 54 km/h
Now, we can calculate the distance traveled in the next 2 hours using the reduced speed:
Distance = Speed × Time
Distance = 54 km/h × 2 hours
Distance = 108 km
Therefore, the car will travel a distance of 108 km in the next 2 hours.

Question 9.A man walks at a speed of 6 kmph for the first half of his journey and then increases his speed by 20% for the second half. If he covers a total distance of 30 km, how long does he take to complete the journey?

• (a) 5 hours
• (b) 6.25 hours
• (c) 4.58 hours
• (d) 3 hours

Answer

(c) 4.58 hours
Let’s calculate the time it takes for the man to complete the journey.
First, let’s determine the distance covered in the first half of the journey. Since the total distance is 30 km, the first half would be half of that, which is 30 km / 2 = 15 km.
To calculate the time taken for the first half of the journey, we use the formula:
Time = Distance / Speed
Time = 15 km / 6 km/h = 2.5 hours
Now, let’s calculate the distance covered in the second half of the journey, which is also 15 km.
To find the increased speed for the second half, we need to add 20% to the original speed of 6 km/h:
Increased Speed = 6 km/h + (6 km/h × 20%)
Increased Speed = 6 km/h + (1.2 km/h) = 7.2 km/h
To calculate the time taken for the second half of the journey, we use the formula:
Time = Distance / Speed
Time = 15 km / 7.2 km/h ≈ 2.08 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 = 2.5 hours + 2.08 hours = 4.58 hours (rounded to two decimal places)
Therefore, the man takes approximately 4.58 hours to complete the entire journey.

Question 10. A train covers a distance of 400 km in 5 hours. If the speed of the train is increased by 25%, how long will it take to cover the same distance?

• (a)2 hours
• (b) 4 hours
• (c)3 hours
• (d)6 hours

Answer

(b) 4 hours
To calculate the new time it will take for the train to cover the same distance with a 25% increase in speed, we first need to find the original speed of the train.
Original speed = Distance / Time
Original speed = 400 km / 5 hours
Original speed = 80 km/h
Now, let’s calculate the increased speed after a 25% increase:
Increased speed = Original speed + (Original speed * 25%)
Increased speed = 80 km/h + (80 km/h * 0.25)
Increased speed = 80 km/h + 20 km/h
Increased speed = 100 km/h
To find the new time, we can use the formula:
New time = Distance / Speed
New time = 400 km / 100 km/h
New time = 4 hours
Therefore, it will take the train 4 hours to cover the same distance with the increased speed of 25%.