Problem:
Every morning Aya goes for a -kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of kilometers per hour, the walk takes her hours, including minutes spent in the coffee shop. When she walks at kilometers per hour, the walk takes her hours and minutes, including minutes spent in the coffee shop. Suppose Aya walks at kilometers per hour. Find the number of minutes the walk takes her, including the minutes spent in the coffee shop.
Solution:
Let be the time in hours that Aya spends in the coffee shop. Then , and . Eliminating gives . Thus and
The requested number of minutes the walk takes Aya is therefore
The problems on this page are the property of the MAA's American Mathematics Competitions