Question

# Latanya will walk her bike from her house to the bike shop , which is 1.5 mi from her house , to get the bike fixed. She expects to wait 30 min for the repair. Then she will ride her bike home. Can she be home in one hour ?

Hint:

### 1. Speed = Distance/time

2. Total time taken = time taken while going to the shop + waiting time + time taken while coming back home

## The correct answer is: Total time taken by Latanya = 69 minutes or 1 hour and 9 minutes

Step-by-step solution:-

Let the time taken by Latanya while going to the bike shop be 'x hours' and while coming back home be 'y hours'.

Now, we know that-

Time = Distance/speed

Time taken by Latanya while going to the bike shop = Distance/speed while going

∴ Time taken by Latanya while going to the bike shop = 1.5 / 3

∴ Time taken by Latanya while going to the bike shop = 0.5 hours

∴ Time taken by Latanya while going to the bike shop = (0.5 × 60) minutes ..................... (1hour = 60 min)

∴ Time taken by Latanya while going to the bike shop = 30 min ........................................ (Equation i)

Time taken by Latanya while coming back home = Distance/speed while going

∴ Time taken by Latanya while coming back home = 1.5 / 10

∴ Time taken by Latanya while coming back home = 0.15 hours

∴ Time taken by Latanya while coming back home = (0.15 × 60) minutes .......................... (1hour = 60 min)

∴ Time taken by Latanya while coming back home = 9 min ........................................ (Equation ii)

Waiting time at the bike shop = 30 min ......................................................................... (Equation iii)

∴ Total time taken by Latanya = Time taken while going to the shop + waiting time + time taken while coming back home

∴ Total time taken by Latanya = 30 + 30 + 9 ................................................................... (From Equations i, ii & iii)

"Final Answer:-

∴ No Latanya will not be able to be home in one hour as the entire journey will take 69 minutes i.e. 9 minutes more than an hour."

∴ Total time taken by Latanya = 69 minutes or 1 hour and 9 minutes

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