Uniform motion problem of the form

[Brigittemcc72184]

I am the mother of an 8th grader trying to figure out the best way to solve and then explain without directly giving her the answer. Tutorials have not helped me!
I understand the formula to be; Distance/Speed/Time

Question;
Two ships were 700mi apart at midnight and were headed directly towards each other. If they collided at 10am, find the speeds of both ships if one was traveling 30mph faster than the other.

D=700mi
T= 12am+10am=10hrs
S=x + y(+30mph)

I’m stuck here. Please help! Ty!!

 

[MarkFL]

Hello, and welcome to FMH!

Distances are in miles and time in hours.

For the slower ship:

[MATH]d_1=v_1t[/MATH]
For the faster ship:

[MATH]d_2=(v_1+30)t[/MATH]
Adding the two equations, we obtain:

[MATH]d_1+d_2=v_1t+(v_1+30)t=2t(v_1+15)[/MATH]
We know:

[MATH]d_1+d_2=700[/MATH]
[MATH]t=10[/MATH]
Can you proceed?

 

[tkhunny]

It is often helpful to separate the travels...

Definitions and Thinking:
Let's use x as the number of miles traveled by Ship #1 prior to collision.
This makes 700 - x an expression for the number of miles traveled by Ship #2 prior to collision

Both ships traveled for 10 hours.

There is one oddity. We are not told which ship is faster. It's just one of them! In this case, it doesn't matter. If we pick Ship #1 to be faster, we'll get one value for x. If we pick Ship #2 to be faster, we'll get a different value for x. You should try it both ways, just to convince yourself that it doesn't change the result.

So, just pick one. I thought maybe Ship #1 is faster, so Speed1 mph = (Speed2 + 30) mph

Formulation:
Ship #1
Distance = Rate * Time
x miles = (Speed1 mph) * (10 hours)
x miles = [(Speed2 + 30) mph] * (10 hours)
Once you see all the units are correct, you can simplify your life by eliminating the symbols. (Be careful with this. Units will save you!)
x = (Speed2 + 30) * 10

Ship #2
Distance = Rate * Time
(700 - x) miles = (Speed2 mph) * (10 hours)
(700 - x) = Speed2 * 10

Can you see a way to proceed?

Solving:
Checking:

It helps to WRITE DOWN EVERYTHING. Don't take mind shortcuts. Let the notation help you. Seriously, look how much I wrote compared to how much you wrote.