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

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Q: 91 (IAS/2002)
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 kilometers does each lady travel in one hour?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,5,2,0,1,5,1

keywords: 

{'travel': [0, 0, 1, 0], 'second lady': [0, 0, 1, 0], 'km': [0, 0, 2, 1], 'many kilometers': [0, 0, 3, 0], 'straight road': [0, 0, 1, 2], 'lady': [1, 0, 2, 2], 'hour': [5, 5, 11, 12], 'first lady': [0, 0, 1, 1], 'ladies': [0, 1, 2, 1]}

Let`s assume the speed of the second lady is x km/hr. Therefore, the speed of the first lady is (x + 2) km/hr.

We know that distance = speed × time.

For the first lady:

Distance traveled = (x + 2) km/hr × (t - 1) hr, where t is the time taken by the second lady to reach A.

For the second lady:

Distance traveled = x km/hr × t hr

According to the given information, the sum of the distances traveled by both ladies is equal to the total distance between A and B, which is 24 km:

(x + 2) km/hr × (t - 1) hr + x km/hr × t hr = 24 km

Simplifying the equation:

(x + 2)(t - 1) + xt = 24

xt + 2t - x - 2 + xt = 24

2xt + 2t - x - 2 = 24

2xt + 2t - x = 26 ............(Equation 1)

Now we can solve this equation to find the values of x and t. Once we have the values, we can calculate the distances traveled by each lady in one hour.

From equation (1), we can rewrite it as:

2xt - x + 2t = 26

x(2t - 1) + 2t = 26

x(2t - 1) = 26 - 2t

x = (26 - 2t)/(2t - 1)

By substituting different values of t, we can find the corresponding value of x. We need to find the values of x and t that satisfy the given conditions (the first lady reaches B one hour before the second lady reaches A).

By trial and error, we find that when t = 3, x = 7.

Therefore, the speed of the second lady is 7 km/hr, and the speed of the first lady is 9 km/hr (7 + 2).

To find the distances traveled by each lady in one hour, we can simply multiply their speeds by 1 hour:

Distance traveled by the first lady = 9 km/hr × 1 hr = 9 km

Distance traveled by the second lady = 7 km/hr × 1 hr = 7 km

Hence, each lady travels 9 km and 7 km, respectively, in one hour.