Time and Distance – Questions and detailed solutions

Question 11. A car covers a distance of 180 km in 3 hours. If the car stops for 15 minutes every hour, what is its average speed in km per hour?

• (a)24 km/h.
• (b) 48 km/h.
• (c) 55 km/h.
• (d) 65 km/h.

Answer

(b) 48 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 180 km in 3 hours.
Now, we need to account for the time spent during the stops. The car stops for 15 minutes every hour, so for a total of 3 hours, there are 3 stops, each lasting for 15 minutes.
Total time spent in stops = 3 stops × 15 minutes/stop = 45 minutes
To convert the 45 minutes into hours, we divide by 60 minutes/hour:
Total time spent in stops = 45 minutes / 60 minutes/hour = 0.75 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 = 3 hours + 0.75 hours = 3.75 hours
Therefore, the car’s average speed is calculated as:
Average speed = Total distance / Total time
Average speed = 180 km / 3.75 hours
Average speed ≈ 48 km/h (rounded to two decimal places)
Therefore, the car’s average speed is approximately 48 km/h.

Question 12.A cyclist travels at a speed of 15 kmph for the first 2 hours and then reduces the speed by 10%. How far will the cyclist travel in the next 3 hours?

• (a) 22 km
• (b) 40.5 km
• (c) 34 km
• (d) 44 km

Answer

(b) 40.5 km
To calculate the distance the cyclist will travel in the next 3 hours, we first need to find the distance covered in the initial 2 hours.
Distance = Speed × Time
Distance = 15 km/h × 2 hours
Distance = 30 km
Next, let’s calculate the reduced speed after decreasing it by 10%.
Reduced Speed = Initial Speed – (Initial Speed × 10%)
Reduced Speed = 15 km/h – (15 km/h × 0.10)
Reduced Speed = 15 km/h – 1.5 km/h
Reduced Speed = 13.5 km/h
Now, we can calculate the distance traveled in the next 3 hours using the reduced speed:
Distance = Speed × Time
Distance = 13.5 km/h × 3 hours
Distance = 40.5 km
Therefore, the cyclist will travel a distance of 40.5 km in the next 3 hours.

Question 13.A boat can cover a certain distance downstream in 4 hours. If the speed of the boat is increased by 50%, how long will it take to cover the same distance downstream?

• (a) 2.67 hours
• (b)2.55 hours
• (c)3.10 hours
• (d)3.45 hours

Answer

(a) 2.67 hours
To calculate the new time it will take for the boat to cover the same distance downstream with a 50% increase in speed, we first need to find the original speed of the boat.
Let’s denote the original speed of the boat as “s” and the time taken to cover the distance downstream as “t.”
The boat covers the distance downstream in 4 hours, so we have:
Distance = Speed × Time
Distance = s × 4
Now, let’s consider the scenario where the speed of the boat is increased by 50%. The new speed would be:
New Speed = Original Speed + (Original Speed × 50%)
New Speed = s + (s × 0.5) = s + 0.5s = 1.5s
To calculate the new time, we can rearrange the formula:
Time = Distance / Speed
Time = (s × 4) / (1.5s)
Time = 4 / 1.5
Time ≈ 2.67 hours
Therefore, it will take the boat approximately 2.67 hours to cover the same distance downstream with the increased speed of 50%.

Question 14. A train covers a distance of 600 km in 7 hours. If it travels at a speed of 90 kmph for the first 2 hours and then reduces its speed by 30%, what will be its average speed for the entire journey?

• (a)65 km/h
• (b)55.71 km/h
• (c)80.71 km/h
• (d) 70.71 km/h

Answer

(d) 70.71 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 600 km in 7 hours.
First, let’s calculate the distance covered in the first 2 hours at a speed of 90 km/h:
Distance = Speed × Time
Distance = 90 km/h × 2 hours
Distance = 180 km
Next, let’s calculate the distance covered in the remaining time, which is 7 hours – 2 hours = 5 hours.
To find the reduced speed after decreasing it by 30%, we subtract 30% of the initial speed from the initial speed:
Reduced Speed = Initial Speed – (Initial Speed × 30%)
Reduced Speed = 90 km/h – (90 km/h × 0.30)
Reduced Speed = 90 km/h – 27 km/h
Reduced Speed = 63 km/h
To calculate the distance covered in the remaining 5 hours at a reduced speed of 63 km/h:
Distance = Speed × Time
Distance = 63 km/h × 5 hours
Distance = 315 km
Now, we can calculate the total distance covered:
Total Distance = Distance in first 2 hours + Distance in remaining 5 hours
Total Distance = 180 km + 315 km
Total Distance = 495 km
To calculate the average speed, we divide the total distance by the total time:
Average Speed = Total Distance / Total Time
Average Speed = 495 km / 7 hours
Average Speed = 70.71 km/h (rounded to two decimal places)

Question 15.A car travels at a speed of 80 kmph for the first 5 hours and then reduces its speed by 15%. How far will it travel in the next 4 hours?

• (a)200 km
• (b)312 km
• (c)412 km
• (d) 272 km

Answer

(d) 272 km
To calculate the distance the car will travel in the next 4 hours, we first need to find the distance it covered in the initial 5 hours.
Distance = Speed × Time
Distance = 80 km/h × 5 hours
Distance = 400 km
Next, let’s calculate the reduced speed after decreasing it by 15%.
Reduced Speed = Initial Speed – (Initial Speed × 15%)
Reduced Speed = 80 km/h – (80 km/h × 0.15)
Reduced Speed = 80 km/h – 12 km/h
Reduced Speed = 68 km/h
Now, we can calculate the distance traveled in the next 4 hours using the reduced speed:
Distance = Speed × Time
Distance = 68 km/h × 4 hours
Distance = 272 km
Therefore, the car will travel a distance of 272 km in the next 4 hours.