Time and Distance – Questions and detailed solutions

Question 46.A car travels at a speed of 60 kmph for the first 2 hours, 50 kmph for the next 3 hours, and 70 kmph for the remaining distance. If the total distance covered is 320 km, how long does the car take to complete the journey?

• (a)6.12 hours
• (b)7.55 hours
• (c)4.10 hours
• (d) 5.71 hours

Answer

(d) 5.71 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 = 2 hours
Distance = Speed × Time = 60 km/h × 2 hours = 120 km
Second part:
Speed = 50 km/h
Time = 3 hours
Distance = Speed × Time = 50 km/h × 3 hours = 150 km
Third part:
Speed = 70 km/h
Distance = Total distance – (Distance covered in the first part + Distance covered in the second part) Distance = 320 km – (120 km + 150 km) = 50 km Time = Distance / Speed = 50 km / 70 km/h ≈ 0.71 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 = 2 hours + 3 hours + 0.71 hours ≈ 5.71 hours
Therefore, the car takes approximately 5.71 hours to complete the entire journey.

Question 47.A boat can travel a certain distance downstream in 6 hours. If it covers the same distance upstream in 12 hours, what is the speed of the boat in still water and the speed of the stream?

• (a) 10 kmph and 3 kmph.
• (b) 9 kmph and 4 kmph.
• (c) 8 kmph and 5 kmph.
• (d) 12 kmph and 2 kmph.

Answer

Let the speed of the boat in still water be x kmph and the speed of the stream be y kmph.

The speed of the boat downstream is x+y kmph and the speed of the boat upstream is x−y kmph.

The boat travels a certain distance downstream in 6 hours. This means that the distance traveled is 6(x+y) km.

The boat travels the same distance upstream in 12 hours. This means that the distance traveled is 12(x−y) km.

Since the boat travels the same distance downstream and upstream, we have 6(x+y)=12(x−y).

Solving for x, we get x=12 kmph.

Solving for y, we get y=2 kmph.