Question

You hike up a hill at 4 km/h. You hike down at 6 km/h. Your hiking trip took 3 hours. How much time did it take you to hike up the hill?

Answer 1

It takes 1.8 hours to go up the hill (and 1.2 hours to come back down).

Explanation:

We know that the distance you hiked we the same in both trips. This causes us to use the relation

`d = v* t`

If we write `t_1` as the time for the trip up the hill, then the distance travelled up is

`4 * t_1`

and the trip down is

`6 * (3-t_1)`

The crucial thing is to realize we don't need a second variable for `t_2`, as it must equal `3-t_1` hours.

The above relations must be equal, as they both describe the equal distances of the trips up and down the hill.

Therefore: `4*t_1=6*(3-t_1)` or,

`4*t_1=18-6*t_1`

`10t_1 = 18`

`t_1 = 1.8` hours

Answer 2

The answer is 1.8 hours.

Explanation:

Using the rate of change formula,

`"rate"="distance"/"time"`

or simply

`r=d/t`,

we can get the formula for distance:

`r=d/t=>d=rt`

Now we can set up an equation with our unknowns:

`D=4"km"/"h"*t`

In this equation, `t` is the time it took to hike up the hill. We can also set up another equation with the time as `3-t` because we know that whatever time the "up" distance didn't use, the "down" distance will:

`D=6"km"/"h"*(3-t)`

Now we can set these two equations equal to each other:

`4cancel("km"/"h")t=6cancel("km"/"h")*(3-t)`

`4t=6(3-t)`

`4t=18-6t`

`10t=18`

`t=18/10=1.8`

Since `t` is the amount of time it took to hike up the hill, the answer is 1.8 hours.