How to solve for distance and original speed when given time, and improved speed and time?

The full question is:

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 6 minutes. How many kilometers long is the loop? (Round your answer to two decimal places.)

1 Answer
A08
Jan 8, 2018

I found it easier to work with fraction and convert the answer to desired accuracy. I also found it convenient to work in given units rather than SI units as the answer is required to be given in #km#

Explanation:

Let Sarah's original speed be #=u" kmh"^-1#
Let length of loop be #=L" km"#
Time taken to complete the loop#=2" h "50" m"=2+50/60=17/6" h"#
Distance time equation is

#17/6u=L# .....(1)

Increase speed #=u+1" kmh"^-1#
Time taken to complete the loop#=2" h "44" m"=2+44/60=2+11/15=41/15" h"#
Distance time new equation is

#41/15(u+1)=L#

Inserting value of #u# in terms of #L# from (1) in (2) we get

#41/15(6/17L+1)=L#
#=>41(6/17L+1)=15L#
#=>246/17L+41=15L#
#=>246L+697=255L#
#=>9L=697#
#=>L=77.44" km"#

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