If x is the cost of bowling per hour, and y is the total cost, then the money spent by Sharon was y = 4x + 11.

The total money spent by Ethan was y = 5x + 10.

Use substitution method (easy)to find out how much did each one spend and how many hours did each one bowl.

Equate them across each other to get

4x + 11 = 5x + 10

-5x + 4x = -11 + 10

-x = -1

x = 1

So they each both bowled for 1 hour.

Plugging in x = 1, in y = 4x + 11, we get y = 4 + 11= 15

And they spent $!5.

I found an answer from www.scientificamerican.com

The Bicycle Problem That Nearly Broke Mathematics - Scientific ...

Jul 20, 2016 **...** His **time at the** US Geological Survey was part of **an** internship, **not a** full-**time** job. ... **Together**, the researchers **went** on to crack **a** century-old debate about what ... Bicycles, he says, **are** “**a** math problem that happens to relate to ... Whipple modelled the bicycle as four rigid objects — **two** wheels, **a** frame with ...

For more information, see The Bicycle Problem That Nearly Broke Mathematics - Scientific ...