# Question fd377

Jan 25, 2018

The fire is about 80 km from the base.

#### Explanation:

Let's use d as the variable name for the one-way distance. The flight's first phase consumed time ${t}_{1}$ flying at 240 km/hr and time ${t}_{2}$ flying at 320 km/hr. The total of those 2 time periods is

t_"total" = t_1 + t_2 = 35 cancel("minutes")*((1 hr)/(60 cancel("minutes"))) = 0.583 hrs

We need expressions for ${t}_{1} \mathmr{and} {t}_{2}$.

t_1 = d/(240 "km"/"hr")" " and " "t_2 = d/(320 "km"/"hr")

Going back to the equation for ${t}_{\text{total}}$, we will put in the above expressions for the 2 time periods.

t_"total" = t_1 + t_2 = d/(240 "km"/"hr")" "+ " "d/(320 "km"/"hr")= 0.583 hrs#

Now, a bunch of algebra ...

$0.004167 \text{hr"/"km"*d" "+ " "0.003125 "hr"/"km} \cdot d = 0.583 h r s$

$0.007292 \text{hr"/"km} \cdot d = 0.583 h r s$

$d = \left(0.583 \text{hrs")/(0.007292 "hr"/"km}\right) = 79.95 k m$

I hope this helps,
Steve