Respuesta :
Answer:
Distance between NJH and Jack's home = 7.10 miles
Distance between NJH and Finn's home = (14-7.10) = 6.9 miles
Step-by-step explanation:
Given:
Jack lives east of NJH and Finn lives west of NJH.
Distance between Jack and Finn's home = 14 miles
Average speed of Jack = 7 mph
Average speed of Finn = 9 mph
Let the distance between Jack's house and NJH is '(x)' miles.
So the distance between Finn's house and NJH is '(14-x)' miles.
According to the question:
Time taken by both Finn and Jack are equal to reach home.
Considering [tex]t_1[/tex] is the time taken by Jack and [tex]t_2[/tex] is the time taken by Finn to reach home.
So,
⇒ [tex]t_1=t_2[/tex]
We have to find the time taken.
⇒ Time taken by Jack. ⇒ Time taken by Finn.
⇒ [tex]t_1=\frac{distance}{speed}[/tex] ⇒ [tex]t_2=\frac{distance}{speed}[/tex]
⇒ [tex]t_1=\frac{x}{7}[/tex] mph ⇒ [tex]t_2=(\frac{14-x}{9} + \frac{15\ min}{60\ min})[/tex] mph ...15 min extra
Equating both [tex]t_1[/tex] and [tex]t_2[/tex] :
⇒ [tex]t_1=t_2[/tex]
⇒ [tex]\frac{x}{7} =\frac{14-x}{9} +\frac{1}{4}[/tex]
⇒ [tex]\frac{x}{7} =\frac{56-4x+9}{36}[/tex]
⇒ [tex]\frac{x}{7} =\frac{65-4x}{36}[/tex]
⇒ Cross multiplying.
⇒ [tex]x(36)=7(65-4x)[/tex]
⇒ [tex]36x=455-28x[/tex]
⇒ [tex]36x+28x=455[/tex]
⇒ [tex]64x=455[/tex]
⇒ [tex]x=\frac{455}{64}[/tex]
⇒ [tex]x=7.10[/tex] miles
Distance between NJH and Jack's home = (x) = 7.10 miles
Distance between NJH and Finn's home = (14-x) = (14-7.10) = 6.9 miles
