Question

If Laisha walks for 1 hour and cycles for 2 hours, she can travel 33 km. But if she walks for 2 hours and cycles for 1 hour, she can cover 24 km. What are her walking and cycling speeds?

Answer 1

Here,

Let Laisha’s walking speed = x km/h,

And Laisha’s cycling speed = y km/h,

According to the given condition, forming equations,

(1) If she walks 1 hour and cycles 2 hours, she covers 33 km:

x(1) + y(2) = 33

x + 2y = 33     ...(i)

(2) If she walks 2 hours and cycles 1 hour, she covers 24 km:

x(2) + y(1) = 24

2x + y = 24     ...(ii)

Let’s multiply equation (i) by 2:

2(x + 2y) = 2(33)

2x + 4y = 66     ...(iii)

Now, subtracting equation (ii) from equation (iii):

(2x + 4y) − (2x + y) = 66 − 24

2x + 4y − 2x − y = 14

3y = 42

y = `42/3`

∴ y = 14

Substituting y = 14 into equation (i):

x + 2(14) = 33

x + 28 = 33

x = 33 − 28

∴ x = 5

Hence, Walking speed is 5 km/h, and Cycling speed is 14 km/h.