Answer:
The length of the loop is approximately 49.58 km.
Step-by-step explanation:
Given:
Time required to ride bicycle in loop = 2 hours and 30 mins
Now we know that;
60 mins = 1 hour
30 mins =0.5 hour
so 2 hour and 30 mins = ![2+0.5 = 2.5\ hrs](https://tex.z-dn.net/?f=2%2B0.5%20%3D%202.5%5C%20hrs)
∴ Time required to ride bicycle in loop = 2.5 hrs
Let the speed at which she is riding the bicycle be 's'.
and let Total distance of the loop be 'd'
Now we know that;
Distance is given by speed multiplied by time.
framing in equation form we get;
![d =2.5s \ \ \ \ equation \ 1](https://tex.z-dn.net/?f=d%20%3D2.5s%20%5C%20%5C%20%5C%20%5C%20equation%20%5C%201)
Now Given:
If she increase the speed by 1 km/hr, it would reduce her time around the loop by 7 minutes.
Hence we can say;
Speed =![s+1](https://tex.z-dn.net/?f=s%2B1)
Also time will be reduce to 7 mins.
7 mins =0.12 hrs
Now time = 2.5-0.12 =2.38
Again Distance is given by speed multiplied by time.
framing in equation form we get;
![d =2.38(s+1) \ \ \ \ equation \ 2](https://tex.z-dn.net/?f=d%20%3D2.38%28s%2B1%29%20%5C%20%5C%20%5C%20%5C%20equation%20%5C%202)
Now distance is same for both so we will calculate the speed by equating the equations.
![2.5s = 2.38(s+1)\\\\2.5s=2.38s+2.38\\\\2.5s-2.38s =2.38\\\\0.12s= 2.38\\\\s =\frac{2.38}{0.12} \approx 19.83\ km/hr](https://tex.z-dn.net/?f=2.5s%20%3D%202.38%28s%2B1%29%5C%5C%5C%5C2.5s%3D2.38s%2B2.38%5C%5C%5C%5C2.5s-2.38s%20%3D2.38%5C%5C%5C%5C0.12s%3D%202.38%5C%5C%5C%5Cs%20%3D%5Cfrac%7B2.38%7D%7B0.12%7D%20%5Capprox%2019.83%5C%20km%2Fhr)
Now Speed = 19.83 km/hr
Length of the loop (d) = ![19.83\times 2.5 = 49.58 \ km](https://tex.z-dn.net/?f=19.83%5Ctimes%202.5%20%3D%2049.58%20%5C%20km)
Hence the length of the loop is approximately 49.58 km.