Time and Distance – Questions and detailed solutions

Question 26. A person crosses a 500 m long bridge in 2 minutes. What is his speed in meters per second?

• (a) 3.12
• (b) 4.167
• (c) 4.443
• (d) 5.215

Answer

(b) 4.167
To calculate the speed in meters per second, we need to convert the time from minutes to seconds.
1 minute is equal to 60 seconds.
So, 2 minutes is equal to 2 x 60 = 120 seconds.
Now, we can calculate the speed:
Speed = Distance / Time
Speed = 500 meters / 120 seconds
Speed ≈ 4.167 meters per second
Therefore, the person’s speed is approximately 4.167 meters per second.

Question 27.A train traveling at a speed of 90 kmph crosses a platform in 36 seconds. If the length of the platform is 300 meters, what is the length of the train?

• (a) 400 meters
• (b) 210 meters
• (c) 600 meters
• (d)550 meters

Answer

(c) 600 meters
To find the length of the train, we need to consider the time it takes to cross the platform and the relative speed between the train and the platform.
The train crosses the platform in 36 seconds, and the length of the platform is 300 meters.
Let’s denote the length of the train as “L.”
The distance traveled by the train to cross the platform consists of the length of the train itself and the length of the platform:
Distance = Length of train + Length of platform
Distance = L + 300 meters
To calculate the time taken to cover this distance, we can use the formula:
Time = Distance / Speed
Time = (L + 300 meters) / 90 km/h
To simplify the calculation, we need to convert the speed from km/h to meters per second.
1 km/h is equal to 1000 meters / 3600 seconds ≈ 0.2778 meters per second.
So, the speed of the train is approximately 90 km/h × 0.2778 meters per second ≈ 25 meters per second.
Now, we can rewrite the equation for time as:
Time = (L + 300 meters) / 25 meters per second
Given that the time is 36 seconds, we can set up the equation:
36 = (L + 300) / 25
Simplifying the equation, we can multiply both sides by 25:
900 = L + 300
Subtracting 300 from both sides, we find:
L = 900 – 300
L = 600 meters
Therefore, the length of the train is 600 meters.

Question 28. A car travels a distance of 480 km in 6 hours. If it covers half the distance at a speed of 60 kmph and the other half at a speed of 80 kmph, what is the average speed of the car for the entire journey?

• (a) 50 km/h
• (b) 45 km/h
• (c) 68.57 km/h
• (d) 35.35 km/h

Answer

(c) 68.57 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 car travels a distance of 480 km in 6 hours.
Let’s break down the journey into two halves:
In the first half, the car covers half the distance, which is 480 km / 2 = 240 km, at a speed of 60 km/h.
To calculate the time taken for the first half of the journey, we use the formula:
Time = Distance / Speed
Time = 240 km / 60 km/h = 4 hours
In the second half, the car covers the remaining half of the distance, which is also 240 km, at a speed of 80 km/h.
To calculate the time taken for the second half of the journey, we use the formula:
Time = Distance / Speed
Time = 240 km / 80 km/h = 3 hours
Now, we can calculate the total time taken for the entire journey:
Total Time = Time for First Half + Time for Second Half
Total Time = 4 hours + 3 hours = 7 hours
Therefore, the car’s average speed is calculated as:
Average Speed = Total Distance / Total Time
Average Speed = 480 km / 7 hours
Average Speed ≈ 68.57 km/h (rounded to two decimal places)
Therefore, the average speed of the car for the entire journey is approximately 68.57 km/h.

Question 29. A bus covers a certain distance at a speed of 72 kmph in 6 hours. How long will it take to cover the same distance at a speed of 60 kmph?

• (a) 40 km/h.
• (b) 50 km/h.
• (c) 60 km/h.
• (d) 70 km/h.

Answer

(c) 60 km/h.
To find out how long it will take for the bus to cover the same distance at a speed of 60 km/h, we need to compare the time taken at the original speed of 72 km/h and the desired speed of 60 km/h.
Let’s denote the original time taken as “t1” and the desired time taken as “t2”. We know that the distance covered is the same in both cases.
Distance = Speed × Time
Since the distance covered is the same, we have:
72 km/h × t1 = 60 km/h × t2
Simplifying the equation:
t1 = (60 km/h × t2) / 72 km/h
t1 = (5/6) × t2
Therefore, the time taken at the original speed is equal to five-sixths of the time taken at the desired speed.
Given that the original time taken is 6 hours, we can set up the equation:
6 = (5/6) × t2
To solve for t2, we multiply both sides by 6/5:
6 × (6/5) = t2
t2 = 7.2 hours
Therefore, it will take the bus 7.2 hours to cover the same distance at a speed of 60 km/h.

Question 30. A person walks at a speed of 6 kmph for the first 2 hours, 8 kmph for the next 3 hours, and 10 kmph for the remaining distance. If the total distance covered is 80 km, how long does the person take to complete the journey?

• (a)8.3 hours
• (b)7.5 hours
• (c)8.5 hours
• (d) 9.4 hours

Answer

(d) 9.4 hours
To calculate the time taken for the person to complete the journey, we need to find the distance covered at each speed and then sum up the individual times.
Let’s break down the journey into three parts based on the different speeds:
First part:
Speed = 6 km/h
Time = 2 hours
Distance = Speed × Time = 6 km/h × 2 hours = 12 km
Second part:
Speed = 8 km/h
Time = 3 hours
Distance = Speed × Time = 8 km/h × 3 hours = 24 km
Third part:
Speed = 10 km/h
Distance = Total distance – (Distance covered in first part + Distance covered in second part)
Distance = 80 km – (12 km + 24 km) = 44 km
Time = Distance / Speed = 44 km / 10 km/h = 4.4 hours
Now, we can calculate the total time taken by summing up the times for each part:
Total Time = Time for first part + Time for second part + Time for third part Total Time = 2 hours + 3 hours + 4.4 hours = 9.4 hours
Therefore, the person takes approximately 9.4 hours to complete the entire journey.