Time and Distance – Questions and detailed solutions

Question 31. A train covers a distance of 600 km in 8 hours. If it covers half the distance at a speed of 80 kmph and the other half at a speed of 100 kmph, what is the average speed of the train for the entire journey?

• (a)92.12 km/h.
• (b)87.5 km/h.
• (c) 88.89 km/h.
• (d)71.85 km/h.

Answer

(c) 88.89 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 8 hours.
Let’s break down the journey into two halves:
In the first half, the train covers half the distance, which is 600 km / 2 = 300 km, at a speed of 80 km/h.
To calculate the time taken for the first half of the journey, we use the formula:
Time = Distance / Speed
Time = 300 km / 80 km/h = 3.75 hours
In the second half, the train covers the remaining half of the distance, which is also 300 km, at a speed of 100 km/h.
To calculate the time taken for the second half of the journey, we use the formula:
Time = Distance / Speed
Time = 300 km / 100 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 = 3.75 hours + 3 hours = 6.75 hours
Therefore, the train’s average speed is calculated as:
Average Speed = Total Distance / Total Time
Average Speed = 600 km / 6.75 hours
Average Speed ≈ 88.89 km/h (rounded to two decimal places)
Therefore, the average speed of the train for the entire journey is approximately 88.89 km/h.

Question 32. A car travels at a speed of 60 kmph for the first 4 hours, 50 kmph for the next 3 hours, and 40 kmph for the remaining distance. If the total distance covered is 350 km, how long does the car take to complete the journey?

• (a) 5 hours
• (b) 6 hours
• (c) 7 hours
• (d) 8 hours

Answer

(c) 7 hours
To calculate the time taken for the car 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 = 60 km/h Time = 4 hours Distance = Speed × Time = 60 km/h × 4 hours = 240 km
Second part:
Speed = 50 km/h Time = 3 hours Distance = Speed × Time = 50 km/h × 3 hours = 150 km
Third part:
Speed = 40 km/h Distance = Total distance – (Distance covered in the first part + Distance covered in the second part) Distance = 350 km – (240 km + 150 km) = -40 km (negative value indicates that the remaining distance is less than zero)
Since the remaining distance is negative, it means that the car has already covered the total distance of 350 km in the first two parts. Therefore, there is no remaining distance to cover in the third part.
Now, we can calculate the total time taken by summing up the times for each part:
Total Time = Time for the first part + Time for the second part Total Time = 4 hours + 3 hours = 7 hours
Therefore, the car takes approximately 7 hours to complete the entire journey.

Question 33.A boat can travel a certain distance downstream in 5 hours. If it covers the same distance upstream in 10 hours, what is the speed of the boat in still water and the speed of the stream?

• (a) 3,4
• (b) 5,4
• (c) 2,8
• (d) None of the above

Answer

(d) None of the above
Let’s denote the speed of the boat in still water as “b” and the speed of the stream as “s”.
When the boat travels downstream, it benefits from the stream’s current, so its effective speed is increased.
When the boat travels upstream, it has to overcome the stream’s current, so its effective speed is decreased.
We can set up two equations based on the given information:
Downstream speed = Boat speed + Stream speed Upstream speed = Boat speed – Stream speed
Given that the distance covered downstream is the same as the distance covered upstream, we can equate the distances:
Downstream speed × Time downstream = Upstream speed × Time upstream
(b + s) × 5 = (b – s) × 10
Expanding the equation:
5b + 5s = 10b – 10s
Combining like terms:
5s + 10s = 10b – 5b
15s = 5b
Dividing both sides by 5:
3s = b
So, we have the relationship: b = 3s.
Since we have one equation with two variables, we cannot determine the exact values of b and s. However, we can express the relationship between them.
Therefore, the speed of the boat in still water (b) is three times the speed of the stream (s).

Question 34. A train covers a distance of 800 km in 10 hours. If it covers half the distance at a speed of 80 kmph and the other half at a speed of 100 kmph, what is the average speed of the train for the entire journey?

• (a) 87.5 km/h.
• (b) 90 km/h.
• (c) 88.89 km/h.
• (d) 92.65 km/h.

Answer

(c) 88.89 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 covers a distance of 800 km in 10 hours.
Let’s break down the journey into two halves:
In the first half, the train covers half the distance, which is 800 km / 2 = 400 km, at a speed of 80 km/h.
To calculate the time taken for the first half of the journey, we use the formula:
Time = Distance / Speed
Time = 400 km / 80 km/h = 5 hours
In the second half, the train covers the remaining half of the distance, which is also 400 km, at a speed of 100 km/h.
To calculate the time taken for the second half of the journey, we use the formula:
Time = Distance / Speed
Time = 400 km / 100 km/h = 4 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 = 5 hours + 4 hours = 9 hours
Therefore, the train’s average speed is calculated as:
Average Speed = Total Distance / Total Time
Average Speed = 800 km / 9 hours
Average Speed ≈ 88.89 km/h (rounded to two decimal places)
Therefore, the average speed of the train for the entire journey is approximately 88.89 km/h.

Question 35. A car travels at a speed of 45 kmph for the first 3 hours, 60 kmph for the next 2 hours, and 30 kmph for the remaining distance. If the total distance covered is 225 km, how long does the car take to complete the journey?

• (a) 82.50 km/h.
• (b) 81.55 km/h.
• (c) 88.89 km/h.
• (d) 75.10 km/h.

Answer

(c) 88.89 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 covers a distance of 800 km in 10 hours.
Let’s break down the journey into two halves:
In the first half, the train covers half the distance, which is 800 km / 2 = 400 km, at a speed of 80 km/h.
To calculate the time taken for the first half of the journey, we use the formula:
Time = Distance / Speed
Time = 400 km / 80 km/h = 5 hours
In the second half, the train covers the remaining half of the distance, which is also 400 km, at a speed of 100 km/h.
To calculate the time taken for the second half of the journey, we use the formula:
Time = Distance / Speed
Time = 400 km / 100 km/h = 4 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 = 5 hours + 4 hours = 9 hours
Therefore, the train’s average speed is calculated as:
Average Speed = Total Distance / Total Time
Average Speed = 800 km / 9 hours
Average Speed ≈ 88.89 km/h (rounded to two decimal places)
Therefore, the average speed of the train for the entire journey is approximately 88.89 km/h.