Each morning Tammy walks the same route to school At onethir

Each morning Tammy walks the same route to school. At one-third way, she passes a drugstore and halfway to school she passes a bicycle shop. At the drugstore, her phone says 7:45 and at the bicycle shop it says 7:50. Assuming she walks at a steady rate, at what time does Tammy reach her school?

Please show work.

Solution

Suppose total distance = x

then she passes a drugstore one-third way : x/3 at 7:45

and she passes a bicycle shop halfway to school : x/2 at 7:50

then distance between drugstore and bicycle shop = x/2 - x/3 = x/6

and time = 7:50 - 7:45 = 5 minutes

So, x/6 distance cover in 5 minutes

then x distance cover = 5 * 6 = 30 minutes

then time to reach her school = 7:50 + 30/2 = 7:50 + 15 minutes = 8:05