Question #fd377

1 Answer
Jan 25, 2018

Answer:

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 and t_2#.

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

Going back to the equation for #t_"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 "hr"/"km"*d" "+ " "0.003125 "hr"/"km"*d = 0.583 hrs#

#0.007292 "hr"/"km"*d = 0.583 hrs#

#d = (0.583 "hrs")/(0.007292 "hr"/"km") = 79.95 km#

I hope this helps,
Steve