Respuesta :
Answer:
Her speed driving in nice weather is 50 mph and in thunderstorm is 32 mph.
Step-by-step explanation:
Barbara drives 50 miles in clear weather and then encounters a thunderstorm for the last 16 miles.
Suppose, her speed in nice weather is [tex]x[/tex] mph.
As she drives 18 mph slower through the thunderstorm than she does in clear weather, so her speed in thunderstorm will be: [tex](x-18) mph[/tex]
We know that, [tex]Time = \frac{Distance}{Speed}[/tex]
So, the time of driving in clear weather [tex]=\frac{50}{x}[/tex] hours
and the time of driving in thunderstorm [tex]=\frac{16}{x-18}[/tex] hours.
Given that, the total time for the trip is 1.5 hours. So, the equation will be......
[tex]\frac{50}{x}+ \frac{16}{x-18}=1.5 \\ \\ \frac{50x-900+16x}{x(x-18)}=1.5\\ \\ \frac{66x-900}{x(x-18)}=1.5 \\ \\ 1.5x(x-18)=66x-900\\ \\ 1.5x^2-27x=66x-900\\ \\ 1.5x^2-93x+900=0\\ \\ 1.5(x^2 -62x+600)=0\\ \\ x^2 -62x+600=0\\ \\ (x-50)(x-12)=0[/tex]
Using zero-product property.........
[tex]x-50=0\\ x=50\\ \\ and\\ \\ x-12=0\\ x=12[/tex]
We need to ignore [tex]x=12[/tex] here, otherwise the speed in thunderstorm will become negative.
So, her speed driving in nice weather is 50 mph and her speed driving in thunderstorm is (50-18) = 32 mph
