Time and Distance – Questions and detailed solutions

Question 41. A boat can travel a certain distance downstream in 3 hours. If it covers the same distance upstream in 6 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 6.5 km/hr and the speed of the stream is 1.5 km/hr.
• (b) speed of the boat in still water is 7.5 km/hr and the speed of the stream is 1.5 km/hr.
• (c) speed of the boat in still water is 8.5 km/hr and the speed of the stream is 1.5 km/hr.
• (d) speed of the boat in still water is 4.5 km/hr and the speed of the stream is 1.5 km/hr.

Answer

(d) speed of the boat in still water is 4.5 km/hr and the speed of the stream is 1.5 km/hr.
The speed of the boat in still water is 4.5 km/hr and the speed of the stream is 1.5 km/hr.
Let x be the speed of the boat in still water and y be the speed of the stream.
The speed of the boat downstream is x + y and the speed of the boat upstream is x – y.
The distance traveled downstream in 3 hours is 3(x + y) and the distance traveled upstream in 6 hours is 6(x – y).
Since the boat travels the same distance downstream and upstream, we have 3(x + y) = 6(x – y).
Solving for x, we get x = 4.5.
Substituting x = 4.5 into 3(x + y) = 6(x – y), we get y = 1.5.
Therefore, the speed of the boat in still water is 4.5 km/hr and the speed of the stream is 1.5 km/hr.

Question 42.A train covers a distance of 300 km in 4 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) 85.55 km/h.
• (b) 88.89 km/h.
• (c) 86.45 km/h.
• (d) 89.99 km/h.

Answer

(b) 88.89 km/h.
To find the average speed of the entire journey, we need to divide the total distance by the total time. Here, the total distance is 300 km.

The total time is calculated as follows:

The train covers the first half of the journey (150 km) at a speed of 80 km/h, so the time taken for this part is distance/speed = 150/80 = 1.875 hours.

Then, the train covers the second half of the journey (150 km) at a speed of 100 km/h, so the time taken for this part is distance/speed = 150/100 = 1.5 hours.

So, the total time taken for the journey is 1.875 + 1.5 = 3.375 hours.

Now, we can calculate the average speed:

Average speed = Total distance / Total time
= 300 km / 3.375 hours
= 88.89 km/h

So, the average speed of the train for the entire journey is approximately 88.89 km/h.

Question 43. A car travels at a speed of 50 kmph for the first 3 hours, 40 kmph for the next 4 hours, and 60 kmph for the remaining distance. If the total distance covered is 350 km, how long does the car take to complete the journey?

• (a) 7.10hours
• (b) 7.55 hours
• (c) 6.65 hours
• (d) 7.67 hours

Answer

(d) 7.67 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 = 50 km/h
Time = 3 hours
Distance = Speed × Time = 50 km/h × 3 hours = 150 km
Second part:
Speed = 40 km/h
Time = 4 hours
Distance = Speed × Time = 40 km/h × 4 hours = 160 km
Third part:
Speed = 60 km/h
Distance = Total distance – (Distance covered in the first part + Distance covered in the second part) Distance = 350 km – (150 km + 160 km) = 40 km Time = Distance / Speed = 40 km / 60 km/h = 0.67 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 = 3 hours + 4 hours + 0.67 hours = 7.67 hours
Therefore, the car takes approximately 7.67 hours to complete the entire journey.

Question 44. A boat can travel a certain distance downstream in 2 hours. If it covers the same distance upstream in 4 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 4 km/hr and the speed of the stream is 5 km/hr
• (b) speed of the boat in still water is 5 km/hr and the speed of the stream is 3 km/hr
• (c) speed of the boat in still water is 7 km/hr and the speed of the stream is 4 km/hr
• (d) speed of the boat in still water is 6 km/hr and the speed of the stream is 2 km/hr

Answer

d) speed of the boat in still water is 6 km/hr and the speed of the stream is 2 km/hr
Let x be the speed of the boat in still water and y be the speed of the current.
The speed of the boat downstream is x+y and the speed of the boat upstream is x−y.
The distance traveled downstream in 2 hours is 2(x+y) and the distance traveled upstream in 4 hours is 4(x−y).
Since the boat travels the same distance downstream and upstream, we have 2(x+y)=4(x−y).
Solving for x, we get x=3y.
Substituting x=3y into 2(x+y)=4(x−y), we get y=2.
Therefore, the speed of the boat in still water is 3×2=6 km/hr and the speed of the stream is 2 km/hr.

Question 45. A train covers a distance of 400 km in 5 hours. If it covers one-third of the distance at a speed of 60 kmph, one-fourth of the distance at a speed of 80 kmph, and the remaining distance at a speed of 100 kmph, what is the average speed of the train for the entire journey?

• (a) 75.55 km/h.
• (b) 70.10 km/h.
• (c) 77.8 km/h.
• (d) 65.25 km/h.

Answer

(c) 77.8 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 400 km in 5 hours.
Let’s break down the journey into three parts:
First part:
Distance = (1/3) * 400 km = 133.33 km Speed = 60 km/h Time = Distance / Speed = 133.33 km / 60 km/h = 2.22 hours
Second part:
Distance = (1/4) * 400 km = 100 km Speed = 80 km/h Time = Distance / Speed = 100 km / 80 km/h = 1.25 hours
Third part:
Distance = Total distance – (Distance covered in the first part + Distance covered in the second part) Distance = 400 km – (133.33 km + 100 km) = 166.67 km Speed = 100 km/h Time = Distance / Speed = 166.67 km / 100 km/h = 1.67 hours
Now, we can calculate the total time taken for the entire journey:
Total Time = Time for the first part + Time for the second part + Time for the third part Total Time = 2.22 hours + 1.25 hours + 1.67 hours = 5.14 hours
Therefore, the train’s average speed is calculated as:
Average Speed = Total Distance / Total Time Average Speed = 400 km / 5.14 hours ≈ 77.8 km/h (rounded to one decimal place)
Therefore, the average speed of the train for the entire journey is approximately 77.8 km/h.