Sarah can bicycle a loop around the north part of Lake Washington in 2 hours and 40 minutes. If she could increase her average speed by 1 km/hr, it would reduce her time around the loop by 6 minutes. How many kilometers long is the loop?

Time equal to distance divided by the speed. In this question, Sarah need 2 hours and 40 minutes (or 160 minutes) to loop around the north part of Lake Washington. The time for the same distance cutted by 6 minutes if the speed increased by 1km/h. The calculation would be:

time = distance/speed

distance = time*speed=

distance1 = distance2

time1*speed1 = time2*speed2

160min*speed1 = (160min-6min) * (speed1+1km/h)

160 speed1 = 154 speed1 + 154km/h

160 speed1 - 154 speed1 = 154km/h

speed1 = 154km/h / 6 = 25.67km/h