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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.)

Respuesta :

Answer:

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