D = r * t based on a boy running up and down a hill

Question

Jack is three times as fast running down a hill than running up the hill. If it takes Jack an hour longer to run up the hill than run down the hill, how long, in hours, does it take Jack to run up the hill?

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I don't even know where to start because when I plug in the information into D = r * t I always get a two variable equation. One variable is the rate - x and the other is the time - y.

Any help would be appreciated.

Answer 1

One unit of time to run down the hill.

Three units of time to run up the hill.

That's two more units to run up than down.

From the problem, those two units are equal to one hour.

So a unit of time is half an hour.

Answer 2

Guide:

$$t_{up}=3t_{down}$$

$$t_{up}=t_{down}+1$$

Solve for $t_{up}$.

Answer 3

$v_0$ is Jack's speed running up the hill

$v_1$ is Jack's speed running down the hill

$v_1$ = 3 * $v_0$

D = $v_0$ * $t_0$

D = $v_1$ * $t_1$

$t_1$ = $t_0$ - 1

Now set the equations equal to each other and substitute $v_1$ with $v_0$ and $t_1$ with $t_0$

$v_0 * t_0 = 3 * v_0 * (t_0 - 1)$

$t_0 = 3 * t_0 - 3$

$t_0 = 3/2$ hours