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Algebra Level 2

Dibyanshu walks a certain distance and rides back in 15 4 \frac{15}{4} hours ,he could ride both ways in 5 2 \frac{5}{2} hours. How many hours would he take to walk both ways?


The answer is 5.

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1 solution

Let w w be the number of hours he walks a certain distance and r r be the number of hours he rides the same distance. Then

w + r = 15 4 w+r=\dfrac{15}{4} ( 1 ) \color{#D61F06}(1)

r + r = 5 2 r+r=\dfrac{5}{2} \implies 2 r = 5 2 2r=\dfrac{5}{2} \implies r = 5 4 r=\dfrac{5}{4} ( 2 ) \color{#D61F06}(2)

subsitute ( 2 ) \color{#D61F06}(2) in ( 1 ) \color{#D61F06}(1) , we have

w + 5 4 = 15 4 w+\dfrac{5}{4}=\dfrac{15}{4}

w = 15 4 5 4 = 10 4 = 5 2 w=\dfrac{15}{4}-\dfrac{5}{4}=\dfrac{10}{4}=\dfrac{5}{2}

Finally,

2 w = 2 ( 5 2 ) = 2w=2\left(\dfrac{5}{2}\right)= 5 \boxed{5}

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