# it takes a plane 40 min longer to fly from boston to los angeles at 525 mi/h than it does to return at 600 mi/h. how far apart are the cities?

distance = rate*time

B to LA = 525mi/hr*t

La to B = 600mi/hr*t

The distance is the same no matter which way we go, but we must ADD 40 minutes to the time for B to LA because the plane is flying slower. So 40 minutes is 40/60 hours and we add that to t. Therefore, B to LA = 525*(t+.6667)

Now set distance = distance.

525*(t+0.66667)= 600*t

Solve for t which gives the time to fly from LA to B. Then time x 600 mi/hr = distance traveled. Post your work if you get stuck.

.2142

actually i don't think that is right sorry.

## No problem! Let's go through the problem again step by step and find the correct solution.

Let's assume that the distance between Boston and Los Angeles is represented by 'd' miles.

We can set up two equations to represent the time it takes to fly from Boston to Los Angeles and from Los Angeles to Boston respectively:

1) Time taken from Boston to Los Angeles: t1

Distance = Rate * Time

d = 525 * t1

2) Time taken from Los Angeles to Boston: t2 (which is 40 minutes less than t1)

Distance = Rate * Time

d = 600 * t2

Now, we can solve these two equations to find the values of t1 and t2.

From equation 1), we can rewrite it as:

t1 = d / 525

Substituting this into equation 2), we have:

d = 600 * (d / 525 - 40/60)

Simplifying the equation:

d = 600 * (d / 525 - 2/3)

Now, let's solve for 'd' by multiplying both sides by 525:

525d = 600d - 400

Bringing 'd' terms to one side, we have:

600d - 525d = 400

75d = 400

Dividing both sides by 75:

d = 400 / 75

d ≈ 5.33

Therefore, the distance between Boston and Los Angeles is approximately 5.33 miles.

Please let me know if there's anything else I can assist you with!