Two ladies simultaneously leave cities A and B connected by a straight road and travel towards each other. The first lady travels 2 km/hr faster than the second lady and reaches B one hour before the second lady reaches A. The two cities A and B are 24 km apart. How many kilometres does each lady travel in one hour? 

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Two ladies simultaneously leave cities A and B connected by a straight road and travel towards each other. The first lady travels 2 km/hr faster than the second lady and reaches B one hour before the second lady reaches A. The two cities A and B are 24 km apart. How many kilometres does each lady travel in one hour?

a) 5 km 3 km

b) 7 km 5 km

c) 8 km 6 km

d) 16 km 14 km

The first lady travels 8 km and the second lady travels 6 km in one hour.

Let’s denote the speed of the second lady as “v” km/hr. Then, the speed of the first lady would be “v + 2” km/hr.

We know that the distance between the two cities is 24 km. Let “t” be the time taken by the second lady to reach city A. Then, the time taken by the first lady to reach city B would be “t – 1” hours because she reaches one hour earlier.

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We can use the formula:

Distance = Speed × Time

For the second lady:

24 = v × t

For the first lady:

24 = (v + 2) × (t – 1)

Now, we can solve these equations to find “v” and “t”.

From the first equation:

v = 24/t

Substitute “v” in the second equation:

24 = (24/t)(t – 1) + 2(t – 1)

24 = 24 – 24/t + 2t – 2

24/t = 2t – 2

24 = 2t² – 2t

2t² – 2t – 24 = 0

Dividing both sides by 2:

t² – t – 12 = 0

Now, we can factorize this quadratic equation:

(t – 4)(t + 3) = 0

So, t = 4 or t = -3.

Since time cannot be negative, t = 4.

Now, we can find “v”:

v = 24/4 = 6 km/hr

So, the speed of the second lady is 6 km/hr, and the speed of the first lady is 6 + 2 = 8 km/hr.

To find the distance traveled in one hour, we just plug in the values:

For the second lady: 6 km/hrFor the first lady: 8 km/hr

So, the answer is option c: 8 km and 6 km.

Time, Speed and Distance

Time, speed, and distance are fundamental concepts in physics and mathematics, especially when dealing with motion. Here’s a brief overview of each:

1. Time: Time is a measure of duration or the progression of events. It is often denoted in units such as seconds, minutes, hours, etc. Time is a fundamental aspect of understanding motion because it helps quantify how long it takes for an object to travel a certain distance.

2. Speed: Speed is a measure of how quickly an object moves. It is the rate of change of distance with respect to time. Mathematically, speed is calculated as:

   Speed = Distance / Time

   The SI unit for speed is meters per second (m/s), although other units such as kilometers per hour (km/h) or miles per hour (mph) are also commonly used depending on the context.

3. Distance: Distance is the amount of space between two points, often measured in meters, kilometers, miles, etc. It is a scalar quantity and can be calculated by multiplying speed by time:

   Distance = Speed×Time

   Alternatively, rearranging the formula for speed:

   Distance = Speed ×Time

Understanding the relationship between these three variables is essential for solving various problems related to motion, such as finding the time taken to travel a certain distance at a given speed, determining the speed required to cover a distance in a specified time, or calculating the distance traveled at a constant speed over a period of time.

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When solving problems involving time, speed, and distance, it’s crucial to ensure that the units are consistent throughout the calculations to obtain accurate results.

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Categories: Math