Question

Sarah can bicycle a loop around the north part of Lake Washington in 2 hours and 30 minutes. If she could increase her average speed by 1 km/hr, it would reduce her time around the loop by 7 minutes. How many kilometers long is the loop?

Answer 1

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 = $2+0.5 = 2.5\ hrs$

∴ 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;

$d =2.5s \ \ \ \ equation \ 1$

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 =$s+1$

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;

$d =2.38(s+1) \ \ \ \ equation \ 2$

Now distance is same for both so we will calculate the speed by equating the equations.

$2.5s = 2.38(s+1)\\\\2.5s=2.38s+2.38\\\\2.5s-2.38s =2.38\\\\0.12s= 2.38\\\\s =\frac{2.38}{0.12} \approx 19.83\ km/hr$

Now Speed = 19.83 km/hr

Length of the loop (d) = $19.83\times 2.5 = 49.58 \ km$

Hence the length of the loop is approximately 49.58 km.