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 = [tex]2+0.5 = 2.5\ hrs[/tex]
∴ 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;
[tex]d =2.5s \ \ \ \ equation \ 1[/tex]
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 =[tex]s+1[/tex]
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;
[tex]d =2.38(s+1) \ \ \ \ equation \ 2[/tex]
Now distance is same for both so we will calculate the speed by equating the equations.
[tex]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[/tex]
Now Speed = 19.83 km/hr
Length of the loop (d) = [tex]19.83\times 2.5 = 49.58 \ km[/tex]
Hence the length of the loop is approximately 49.58 km.
