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

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?

Solution :-

Consider that x km/hr is the walking speed and y km/hr is the cycling speed.

According to the question

When we read question we have two conditions and consider x and y. And write two conditions in two equations.

$\begin{gathered} \blue{\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\: Equation\: is :- \: \begin{cases} &\sf{1x + 2y = 33} \\ \\ &\sf{2x + 1y = 24} \end{cases}\end{gathered}\end{gathered}}\end{gathered}$

Solve the equation

Multiply the equation (1) by 2, we get

♣ 2x + 4y = 66 ————(3)

Now subtract equation (2) from equation (3)

$\sf:\longmapsto{2x + 4y - (2x + 1y) = 66 - 24} \\ \\ \sf:\longmapsto{2x + 4y - 2x - 1y = 42} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf:\longmapsto{3y = 42} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bf:\longmapsto \red{y = 14} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Substitute y = 14 in equation (1)

$\sf:\longmapsto{1x + 2(14) = 33} \\ \\ \sf:\longmapsto{x + 28 = 33} \: \: \: \: \: \: \\ \\ \sf:\longmapsto{x = 33 - 28} \: \: \: \: \: \\ \\ \bf:\longmapsto \red{5} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Answer :

$\begin{gathered} \red{\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:Solution \: is \: - \: \begin{cases} &\sf{x \: = \: 5} \\ \\ &\sf{y \: = \: 14} \end{cases}\end{gathered}\end{gathered}}\end{gathered}$

Therefore, her walking speed is 5km/hr and her cycling speed is 14km/hr.

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