Respuesta :
A motorist travelled to a distant city in 2 hours and returned by another route that is 30 miles longer. On the return trip she travelled 10 miles per hour faster and took 6 minutes longer. Find the length of the shorter route.
180 miles
180 miles
The length of the shorter route at which motorist travelled to a distant city in 2 hours is 180 miles.
What is the speed of a body?
The speed of a body is the rate at which it covers the total distance in the time taken. The speed of the body is given as,
[tex]s=\dfrac{d}{t}[/tex]
Here, (d) is the distance travelled by the body and (t) is time taken by the body to cover that distance.
Let the length of the shorter route is x meters. The motorist travelled to a distant city at this route in 2 hours. thus the speed of the mototist is,
[tex]S_s=\dfrac{x}{2}[/tex]
The distance of the longer route is 30 miles and he took 6 minutes longer than the earliear route (2hours 6 minutes). Thus the speed of the mototist at longer route is,
[tex]S_l=\dfrac{x+30}{2+\dfrac{6}{60}}\\S_l=\dfrac{x+30}{\dfrac{120+6}{60}}\\S_l=\dfrac{(x+30)\times60}{{126}}\\[/tex]
She travelled 10 miles per hour faster at longer route. Thus,
[tex]S_l=S_s+10\\\dfrac{(x+30)\times60}{{126}}=\dfrac{x}{2}+10\\\dfrac{(x+30)\times6}{{21}}=\dfrac{x+20}{2}\\x=180\rm\; miles[/tex]
Hence, the length of the shorter route at which motorist travelled to a distant city in 2 hours is 180 miles.
Learn more about the speed here:
https://brainly.com/question/359790
