Time and Distance – Questions and detailed solutions

Question 36.A train covers a distance of 400 km in 5 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) 60
• (b) 90
• (c) 70
• (d) 80

Answer

(d) 80
The train travels at 80 kmph for 2 hours and at 100 kmph for 2 hours.

The distance traveled at 80 kmph is 160 km.

The distance traveled at 100 kmph is 200 km.

The average speed of the train is 400 km / 5 hours = 80 kmph.

So the answer is 80

Question 37. A car travels at a speed of 40 kmph for the first 4 hours, 30 kmph for the next 3 hours, and 50 kmph for the remaining distance. If the total distance covered is 280 km, how long does the car take to complete the journey?

• (a) 7.6 hours
• (b)6.5 hours
• (c)7.1 hours
• (d)8.5 hours

Answer

(a) 7.6 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 = 40 km/h Time = 4 hours Distance = Speed × Time = 40 km/h × 4 hours = 160 km
Second part:
Speed = 30 km/h Time = 3 hours Distance = Speed × Time = 30 km/h × 3 hours = 90 km
Third part:
Speed = 50 km/h Distance = Total distance – (Distance covered in the first part + Distance covered in the second part) Distance = 280 km – (160 km + 90 km) = 30 km Time = Distance / Speed = 30 km / 50 km/h = 0.6 hours
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 + Time for the third part Total Time = 4 hours + 3 hours + 0.6 hours = 7.6 hours
Therefore, the car takes approximately 7.6 hours to complete the entire journey.

Question 38.A boat can travel a certain distance downstream in 4 hours. If it covers the same distance upstream in 8 hours, what is the speed of the boat in still water and the speed of the stream?

• (a) speed of the boat in still water is 12 kmph and the speed of the stream is 2 kmph
• (b) speed of the boat in still water is 14 kmph and the speed of the stream is 4 kmph
• (c) speed of the boat in still water is 13 kmph and the speed of the stream is 5 kmph
• (d) speed of the boat in still water is 15 kmph and the speed of the stream is 7 kmph

Answer

(a) speed of the boat in still water is 12 kmph and the speed of the stream is 2 kmph
Let the speed of the boat in still water be x kmph and the speed of the stream be y kmph.
The speed downstream is (x+y) kmph, and the speed upstream is (x−y) kmph.
The distance covered downstream in 4 hours is 4(x+y) km, and the distance covered upstream in 8 hours is 8(x−y) km.
Since the boat covers the same distance downstream and upstream, we have 4(x+y)=8(x−y).
Solving for x, we get x=12.
Substituting x=12 into 4(x+y)=8(x−y), we get y=2.
Therefore, the speed of the boat in still water is 12 kmph and the speed of the stream is 2 kmph.

Question 39. A train covers a distance of 500 km in 6 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)81.50 kmph
• (b)75.50 kmph
• (c) 83.33 kmph
• (d)71.50 kmph

Answer

(c) 83.33 kmph
The train travels at 80 kmph for 2.5 hours and at 100 kmph for 2.5 hours.

The distance traveled at 80 kmph is 200 km.

The distance traveled at 100 kmph is 250 km.

The average speed of the train is 500 km / 6 hours = 83.33 kmph.

So the answer is 83.33

Question 40. A car travels at a speed of 55 kmph for the first 5 hours, 65 kmph for the next 2 hours, and 45 kmph for the remaining distance. If the total distance covered is 375 km, how long does the car take to complete the journey?

• (a) 7 hours
• (b)9 hours
• (c)6 hours
• (d)6 hours

Answer

(a) 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 = 55 km/h Time = 5 hours Distance = Speed × Time = 55 km/h × 5 hours = 275 km
Second part:
Speed = 65 km/h Time = 2 hours Distance = Speed × Time = 65 km/h × 2 hours = 130 km
Third part:
Speed = 45 km/h
Distance = Total distance – (Distance covered in the first part + Distance covered in the second part)
Distance = 375 km – (275 km + 130 km) = -30 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 375 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 = 5 hours + 2 hours = 7 hours
Therefore, the car takes approximately 7 hours to complete the entire journey.