Sarah can bicycle a loop around the north part of Lake Washington in 2 hours and 50 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? (Round your answer to two decimal places.)

67.84 km

Step-by-step explanation:

let her initial speed be 'u'

Time with speed u = 2 hours 50 minutes = 2.83 hours

Distance = speed * Time

therefore,

Distance = u * 2.83 ... (1)

when speed increase by 1 km/h

speed, v = u + 1

Time taken = 2 hours 50 minutes - 7 minutes

= 2 hours 43 minutes

= 2.7167 hours

Therefor,

Distance = (u + 1) * 2.7167 ... (2)

since, the distance in both the cases will be same

therefore,

from 1 and 2

u * 2.83 = (u + 1) * 2.7167

or

u * 1.0417 = u + 1

or

0.0417u = 1

or

u = 23.97 km/hr

Therefore,

Distance of loop = u * 2.83

= 23.97 * 2.83

= 67.84 km