Question

6. Aaron will run from home at y mph and walk back at x mph. how much distance does he need to travel to spend a total of t hours walking and jogging. (A) xt/y (B) (x+t)/xy (C) xyt/(x+y) (D) (x+y+t)/xy (E) (y+t)/x-t/y

Answer 1

Answer:

Total distance, $d=\dfrac{xyt}{(x+y)}$

Explanation:

It is given that,

Speed of Aaron from home is y mph and walk back at x mph. Let t is the total time he spend in walking and jogging. Let d is the distance covered.

We he moves from home to destination, time is equal to, $\dfrac{d}{x}$

Similarly, when he move back to home, time taken is equal to $\dfrac{d}{y}$

Total time taken is equal to :

$\dfrac{d}{x}+\dfrac{d}{y}=t$

$d(\dfrac{1}{x}+\dfrac{1}{y})=t$

$d=\dfrac{t}{(\dfrac{1}{x}+\dfrac{1}{y})}$

$d=\dfrac{xyt}{(x+y)}$

So, the distance he speed in walking and jogging is $\dfrac{xyt}{(x+y)}$. Hence, this is the required solution.