Time and Distance – Questions and detailed solutions

Question 16.A man walks at a speed of 5 kmph for the first half of his journey and then increases his speed by 10% for the second half. If he covers a total distance of 20 km, how long does he take to complete the journey?

• (a)4.10 hours
• (b)3.15 hours
• (c) 3.82 hours
• (d)2.25 hours

Answer

(c) 3.82 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 20 km, the first half would be half of that, which is 20 km / 2 = 10 km.
To calculate the time taken for the first half of the journey, we use the formula:
Time = Distance / Speed
Time = 10 km / 5 km/h = 2 hours
Next, let’s calculate the distance covered in the second half of the journey, which is also 10 km.
To find the increased speed for the second half, we need to add 10% to the original speed of 5 km/h:
Increased Speed = 5 km/h + (5 km/h × 10%)
Increased Speed = 5 km/h + (0.5 km/h) = 5.5 km/h
To calculate the time taken for the second half of the journey, we use the formula:
Time = Distance / Speed
Time = 10 km / 5.5 km/h ≈ 1.82 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 hours + 1.82 hours = 3.82 hours (rounded to two decimal places)
Therefore, the man takes approximately 3.82 hours to complete the entire journey.

Question 17.A train covers a distance of 300 km in 4 hours. If the speed of the train is increased by 20%, how long will it take to cover the same distance?

• (a) 3.33 hours
• (b)3.99 hours
• (c)4.33 hours
• (d)4.99 hours

Answer

(a) 3.33 hours
To calculate the new time it will take for the train to cover the same distance with a 20% 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 300 km in 4 hours, so we have:
Distance = Speed × Time
300 km = s × 4
Now, let’s consider the scenario where the speed of the train is increased by 20%. The new speed would be:
New Speed = Original Speed + (Original Speed × 20%)
New Speed = s + (s × 0.20) = s + 0.20s = 1.20s
To calculate the new time, we can rearrange the formula:
Time = Distance / Speed
Time = 300 km / (1.20s)
Now, we need to substitute the original speed in terms of “s” back into the equation.
300 km = s × 4
s = 300 km / 4 = 75 km/h
Substituting this value back into the new time equation:
Time = 300 km / (1.20 × 75 km/h)
Time = 300 km / 90 km/h
Time = 3.33 hours

Question 18.A car covers a distance of 120 km in 2 hours. If the car stops for 10 minutes every hour, what is its average speed in km per hour?

• (a) 61.25 km/h.
• (b) 33.91 km/h.
• (c) 43.89 km/h.
• (d) 51.5 km/h.

Answer

(d) 51.5 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 120 km in 2 hours.
Now, we need to account for the time spent during the stops. The car stops for 10 minutes every hour, so for a total of 2 hours, there are 2 stops, each lasting for 10 minutes.
Total time spent in stops = 2 stops × 10 minutes/stop = 20 minutes
To convert the 20 minutes into hours, we divide by 60 minutes/hour:
Total time spent in stops = 20 minutes / 60 minutes/hour = 0.33 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 hours + 0.33 hours = 2.33 hours
Therefore, the car’s average speed is calculated as:
Average speed = Total distance / Total time
Average speed = 120 km / 2.33 hours
Average speed ≈ 51.5 km/h (rounded to one decimal place)
Therefore, the car’s average speed is approximately 51.5 km/h.

Question 19.A cyclist travels at a speed of 18 kmph for the first 3 hours and then reduces the speed by 15%. How far will the cyclist travel in the next 4 hours?

• (a)51.10 km
• (b)41.10 km
• (c) 61.2 km
• (d)71.20 km

Answer

(c) 61.2 km
To calculate the distance the cyclist will travel in the next 4 hours, we first need to find the distance covered in the initial 3 hours.
Distance = Speed × Time
Distance = 18 km/h × 3 hours
Distance = 54 km
Next, let’s calculate the reduced speed after decreasing it by 15%.
Reduced Speed = Initial Speed – (Initial Speed × 15%)
Reduced Speed = 18 km/h – (18 km/h × 0.15)
Reduced Speed = 18 km/h – 2.7 km/h
Reduced Speed = 15.3 km/h
Now, we can calculate the distance traveled in the next 4 hours using the reduced speed:
Distance = Speed × Time
Distance = 15.3 km/h × 4 hours
Distance = 61.2 km
Therefore, the cyclist will travel a distance of 61.2 km in the next 4 hours.

Question 20.A boat can cover a certain distance downstream in 6 hours. If the speed of the boat is increased by 40%, how long will it take to cover the same distance downstream?

• (a)3.25 hours
• (b)4.10 hours
• (c) 4.29 hours
• (d)5.25 hours

Answer

(c) 4.29 hours
To calculate the new time it will take for the boat to cover the same distance downstream with a 40% 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 6 hours, so we have:
Distance = Speed × Time
Distance = s × 6
Now, let’s consider the scenario where the speed of the boat is increased by 40%. The new speed would be:
New Speed = Original Speed + (Original Speed × 40%)
New Speed = s + (s × 0.40) = s + 0.40s = 1.40s
To calculate the new time, we can rearrange the formula:
Time = Distance / Speed
Time = (s × 6) / (1.40s)
Now, we can simplify the equation by canceling out the “s” terms:
Time = 6 / 1.40
Time ≈ 4.29 hours (rounded to two decimal places)
Therefore, it will take the boat approximately 4.29 hours to cover the same distance downstream with the increased speed of 40%.