It took emily 25 min to rideHer bicycle to the repair shop in one hour and 15 minutes to walk back home. If Emily her bicycle to the repair shop in one hour and 15 minutes to walk back home. If Emily can ride her bicycle 8 km/h faster than she can walk how far is the repair shop from her house?

Answer:the repair shop is 5km from her house.

Step-by-step explanation:

Let x represent the distance of the repair shop from her house.

Let y represent Emily's speed when riding.

Distance = speed * time

It took Emily 25 min to ride her bike to the repair shop. Converting 25 min to hours, it becomes 25/60 = 5/12 hours.

Distance covered,

x = y * 5/12 = 5y/12

It took her 1h 15 min to walk back home. Converting to hours, it becomes 1 + 15/60 = 1 1/4 = 5/4

If she can ride her bike 8km/h faster than she can walk, it means that her speed while walking would be y 8 8

Therefore,

Distance covered,

x = 5/4 (y - 8) = (5y - 40) / 4

Since the distance remains the same, then

5y/12 = (5y - 40) / 4

Crossmultiplying, it becomes

5y * 4 = 12 (5y - 40)

20y = 60y - 480

60y - 20y = 480

40y = 480

y = 480/40 = 12

x = 5y/12 = 5 * 12/12 = 5 km