A girl ran to a store at the rate of 6 miles per hour, and she walked back at the rate of 4 miles per hour.

Question

Thats the rest of the problem:

 

If it took 15 minutes for the round trip, how far away is the store.

Answer 1

distance=rate*time

d=6t

d=4(0.25-t) (15 minutes=0.25 hours)

6t=4(0.25-t)

6t=1-4t

6t+4t=1

10t=1

t=1/10 of an hour

d=6t

d=6(1/10)

d=6/10 or 3/5 of a mile

the store is 6/10 or 3/5 of a mile away

Answer 2

Hello Olivia,

 

This is a distance = rate times time problem

 

We have the following

 

d₁ = distance to store

t₁ = time to store

r₁ = 6 mph 

 

And

 

d₂ = distance back home

t₂ = time home

r₂ = 4 mph

 

Since she ran to the store and then walked back home d₁=d₂

and

r₁t₁ = r₂t₂

6t₁ = 4t₂

we also know that t₁ + t₂ = 15 minutes = .25 hours

Solving for t₁

t₂ = .25-t₁

 

Let's substitute this expression for t₂ in the equation above

6t₁ = 4t₂

6t₁ = 4(.25-t₁)

 

distribute the 4

6t₁ = 1-4t₁

 

add 4t₁ to both sides

10t₁ = 1

 

divide by 10

t₁ = .1

 

Now use this value of t₁ in the distance formula to find the distance to the store.

d₁ = r₁t₁

d₁ = 6(.1) = .6

 

So the store is 6/10 of a mile away