Question

A man walks for $x$ hours at 4 km/hr and then for $y$ hours at $3$ km/hr. If he walks altogether $29$ km in $8$ hours, find the values of $x$ and $y$.

• A. $x=2$ and $y=1$
• B. $x=7$ and $y=2$
• C. $x=6$ and $y=9$
• D. $x=5$ and $y=3$

Answer 1

Answer: (D)

$x=5$ and $y=3$

Speed $=\frac{Distance}{Time}$
Distance travelled for $x$ hours at $4$ km/hr $=$ Speed $\times$ Time$=4x$ km
Distance travelled for $y$ hours at $3$ km/hr $=$ Speed $\times$ Time $=3y$ km
Given, total distance $4x+3y=29$ --- (1)
And Total time $x+y=8$ --- (2)

Multiplying equation $\left(2\right)$ with $4$ we get, $4x+4y=32$ ----- (3)

Subtracting (1) from (3), we get $y=3$

Substituting $y=3$ in (2), we get $x+3=8=>x=5$
Hence, $x=5;y=3$