Distance Rate and Time Word Problems

[princess]

Distance rate time formulas help!
40Kph car 60kph left 3 hours later how long will it take for the 60kph car to catch the 40kph car?
40(x+3) + 60x = x +3 + x
40x +120 + 60X = 2x +3
100x +120 = 2x +3
98x = 117
HELP!

 

[wjm11]

Distance rate time formulas help!
40Kph car 60kph left 3 hours later how long will it take for the 60kph car to catch the 40kph car?

Hi, Princess,

The thing the two cars will have in common when they meet is how for they’ve traveled.
Thus, since d = vt, and where d1, v1, and t1 all refer to the first car’s distance, speed and time,

d1 = v1*t1
d2 = v2*t2
d1 = d2

Therefore, v1*t1 = v2*t2. Also, we know that t2 = t1-3.

Can you take it from here?

 

[princess]

Still have a mental block about finding the time they will catch up to each other. Thankyou for your help. Help!

 

[princess]

Could you please just explain the overall way in which I find the time that they will catch up?
HELP! Princess, thanks.

 

[soroban]

Hello, princess!

A 40 kph car drove off. A 60 kph car left 3 hours later.
How long will it take for the 60kph car to catch the 40kph car?

I have no idea where you got your equation . . .
I don't suppose you drew a picture.

Car A drove for 3 hours at 40 kph; it traveled 120 km.
Then it drove for another \(\displaystyle x\) hours and traveled \(\displaystyle 40x\) km.

            120 km            40x km 
. . . * - - - - - - - - * - - - - - - - - *

Car B drive the same \(\displaystyle x\) hours and travels \(\displaystyle 60x\) km.

                    60x km  
. . . * - - - - - - - - - - - - - - - - - *

Since car B catches up to car A, the distances are equal:
\(\displaystyle \;\;\;120\,+\,40x\;=\;60x\)

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Here's a back-door approach to this problem.

Car B is going 20 kph faster than car A.
It is as if car A is stopped and car B is driving toward it at 20 kph.

Imagine this scenario: car A drives for 3 hours and stops (120 km away).
Car B drives toward it at 20 kph. . . How long will take to catch up?

 

[princess]

Distance Rate Time Formulas

Thank you,
I believe I understand now how to find the time the two will catch up. :lol: Since their distances are the same you put one equals the other.
Once again thank you!
Princess