Two planes leave an airport at noon. If the eastbound plane flies at 560 mph and the westbound plane flies at 500 mph, at what time will they be 2,000 miles apart? Round your answer to the nearest minute.

Question

Shadow · Answer

I have a couple of thoughts on how to approach this. Do you have any ideas though?

Shadow · Answer

I can help you once I know you're here ^-^

getlikeliyiah · Answer

yes i'm still here

Shadow · Answer

Do you have a guess as to how you would start this?

getlikeliyiah · Answer

noon is at 12pm so would i round that up to the nearest minute ?

getlikeliyiah · Answer

The east and the west bounds are different because one is 500 and the other is 560 so it's 60 apart. Would you subtract 60 from 12:00 and round?

getlikeliyiah · Answer

are you still here?

Shadow · Answer

Yes

Shadow · Answer

So first lets recognize what they are asking for. "At what time will they be 2,000 miles apart?" We can solve for this by getting the time it takes for them to be 2000 miles apart, then adding it to 12pm (their departure time).

We can solve for the time it takes for them to be 2000 miles apart by adding their two speeds together. This is because they are moving in opposite directions (with the first one being eastbound, and the second westbound). Since they are moving in opposite directions, their distance apart is increasing in accordance to those speeds. We can simple just add those speeds together to make our lives easier

560 + 500 = 1060

Now, note the formula:

$$D = R \times T$$

Distance is equal to rate multiplied by time.

This is because the rate is a distance over time quantity, example: miles per hour

$$\frac{ mi }{ hour } \times hour$$

You multiply by some quantity of time in the same units(hours) and you get your distance.

Now using that formula and the information that we have, how would you set this up?