Question

Two persons 27 kilometres apart, starting at the same time are together in 9 hours if they walk in the same direction, but 3 hours if they walk in the opposite directions. find out the rate of walking of each?



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Answer 1

$\huge{ \color{pink}{ \colorbox{black}{answer}}}$

Let a = the walking rate of the 1st person which is the fastest walker

let b = the walking rate of the 2nd person

$\large{ \bold{ \underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}}$

$\large{ \sf{ \underline{Given}}}$

9(a - b) = 27

$\large{ \red{(walking \: the \: same \: direction)}}$

3(a + b) = 27

$\large{ \orange{(walking \: the \: opposite \: direction)}}$

$\large{ \green{ \fbox{{on \: simplifying}}}}$

a-b=3

a+b=9

$\large{ \purple{solving}}$

2a = 12

$\large{ \sf{a = \frac{12}{5}}}$

$\large{ \sf{a = 6 \frac{km}{hr} \: \: \: first \: person \: rate \: then \: \: }}$

6 + b = 9

$\large{ \sf{b = 3 \frac{km}{hr} \: \: \: \: second \: person \: rate}}$

hope its help u

Answer 2

Answer:

Hello Santa19!

Let the speed of A=x and B= y km/ hr.

if they move in the same direction then Relative speed = x-y.

if they move in opposite direction their Relative speed = x+y.

$\cancel3 = \frac{ \cancel27 \: ^{9} }{x + y} \: \: \: \: \: \cancel9 = \frac{ { \cancel{27}} \: \: ^{3} }{x - y}$

$x + \cancel y = 9 \: \: \: \: \: \: \: \: x + y = 9\\ \frac{x - \cancel y = 3}{2x = 12} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: y = 3 \\ x = 6 \: put \: in$

Hence their speed is 6 and 3 km/hr.

Hope it helps you from my side