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
is the time taken by Jack and
is the time taken by Finn to reach home.
So,
⇒ ![t_1=t_2](https://tex.z-dn.net/?f=t_1%3Dt_2)
We have to find the time taken.
⇒ Time taken by Jack. ⇒ Time taken by Finn.
⇒
⇒ ![t_2=\frac{distance}{speed}](https://tex.z-dn.net/?f=t_2%3D%5Cfrac%7Bdistance%7D%7Bspeed%7D)
⇒
mph ⇒
mph <em> ...15 min extra </em>
Equating both
and
:
⇒ ![t_1=t_2](https://tex.z-dn.net/?f=t_1%3Dt_2)
⇒ ![\frac{x}{7} =\frac{14-x}{9} +\frac{1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B7%7D%20%3D%5Cfrac%7B14-x%7D%7B9%7D%20%2B%5Cfrac%7B1%7D%7B4%7D)
⇒ ![\frac{x}{7} =\frac{56-4x+9}{36}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B7%7D%20%3D%5Cfrac%7B56-4x%2B9%7D%7B36%7D)
⇒ ![\frac{x}{7} =\frac{65-4x}{36}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B7%7D%20%3D%5Cfrac%7B65-4x%7D%7B36%7D)
⇒ Cross multiplying.
⇒ ![x(36)=7(65-4x)](https://tex.z-dn.net/?f=x%2836%29%3D7%2865-4x%29)
⇒ ![36x=455-28x](https://tex.z-dn.net/?f=36x%3D455-28x)
⇒ ![36x+28x=455](https://tex.z-dn.net/?f=36x%2B28x%3D455)
⇒ ![64x=455](https://tex.z-dn.net/?f=64x%3D455)
⇒ ![x=\frac{455}{64}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B455%7D%7B64%7D)
⇒
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