Im not old enough to take this math :( can someone plz help me with this test thingy.?

Question

Alexis left Miami and drove at a speed of 20 kph. Thomas left 3 hours later and drove at a speed of 30 kph. How long will it take Thomas to catch up to Alexis?

9 hours?
7.5 hours?
6 hours ?



Savannah left Miami and drove at a speed of 47 mph. Timothy left 2 hours later and drove at a speed of 58 mph. How long will it take Timothy to catch up with Savannah?

8.55 hours ?
10.55 hours ?
7.5 hours ?


Two jets leave an airport at the same time in opposite directions. The first jet is traveling at three hundred twenty-three mph and the other at two hundred mph. How long will it take for the jets to be 2,371 miles apart?

4.53 hours
2.37 hours
123 hours


Caleb left New York and drove at a speed of 15 kph. Ryan left 3 hours later and drove at a speed of 20 kph. How long will it take Ryan to catch up with Caleb? ?

12 hours
9 hours
6 hours



I have 15 questions on each lesson, and i have 3 lessons. come on guys, ya gotta help me out lol. thnx

Answer 1

Let Thomas catches Alexis in 't' hours.
Then, distance travelled by Thomas = Speed*Time = 30*t km
Now, distance travelled by Alexis = Speed*Time = 20*(t+3) km

[As Alexis started 3 hrs early so he drove for 3 more hours. So (t+3) comes.]

As Alexis is overtaken by Thomas, the distance travelled by both is same.
So 30t = 20(t+3) or t = 6

So Thomas catches up with Alexis in 6 hours.


Exactly as the first problem, let Timothy catches Savannah in 't' hours.
Then, distance travelled by Timothy = Speed*Time = 58*t mile
Now, distance travelled by Savannah = Speed*Time = 47*(t+2) mile

[As Savannah started 2 hrs early so he drove for 2 more hours. So (t+2) comes.]

As Savannah is overtaken by Timothy, the distance travelled by both is same.
So 58t = 47(t+2) or t = 94/11 = 8.55

So Timothy catches up with Savannah in 8.55 hours.


Third problem:
Speed of first jet = 323 mph
Speed of second jet = 200 mph in opposite direction.
So relative velocity is (323 + 200) = 523 mph.
Time = Distance/Speed = 2371/523 = 4.53 hours


Exactly as the first and second problem, let Ryan catches Caleb in 't' hours.
Then, distance travelled by Ryan = Speed*Time = 20*t mile
Now, distance travelled by Caleb = Speed*Time = 15*(t+3) mile

[As Caleb started 3 hrs early so he drove for 3 more hours. So (t+3) comes.]

As Caleb is overtaken by Ryan, the distance travelled by both is same.
So 20t = 15(t+3) or t = 9

So Ryan catches up with Caleb in 9 hours.

Answer 2

To work out the first one, work out how much distance Alexis travels in the 3 hours that Thomas hasn't. speed x time = distance so 20 x 3 = 60 km. Then notice that the speed difference is 10 km/h because Thomas drives at 30 km/h and Alexis drives at 20 km/h. Thomas has to catch up by 60 km and is travelling 10 km/h faster, so therefore it will take 6 hours to catch up.

For the 2nd one, Savannah drives at a speed of 47 mph, and Tim left 2 hours later, so in that time Savannah goes 94 miles. Again notice the speed difference, 11 mph. The time to catch up is 94 / 11 = 8.55 hours.

For the 3rd one, one jet is travelling at 323 mph and the other at 200 mph so in one hour they are 523 miles apart from each other. For them to be 2371 miles apart you just work out 2371 divided by 523 = about 4.53 hours apart.

For the last one, just use the same method as I mentioned above in the first two Qs, I can't give away everything.

Answer 3

Thomas gains 10 km on Alexis every hour. By the time he sets out, Alexis has gone
20 * 3 = 60 km

So at 10 km / h, Thomas needs
60/10 = 6 hours to catch up.

DanE's solution is correct, except that x hours is the time Alexis has travelled. Thomas travels 3 hours less.

It looks to me as if they're all the same as this, except the jets question is slightly different as they're going in opposite directions. What happens in 1 hour? One goes 323 miles, the other goes 200 miles in the opposite direction, so they are
523 km apart.

How many hours does it take to be 2371 miles apart?
2371/523 = ...


P.S. Sorry I can't come up with a little moralising lecture as some of the other answerers do. I'm sure you must appreciate those!!!

Answer 4

These are all based on rate(time) = distance.

For Alexis: 20t = d
For Thomas: 30(t-3) = d
Since Thomas has to catch up with Alexis, their distances are equal, so
20t = 30(t-3)
20t = 30t - 90
-10t = - 90
t = 9 hours for Alexis
t - 3 = 6 hours for Thomas

The Savannah and Timothy problem is basically the same.

For the jets, their combined distance will be 2371.
Jet 1: 323t = d
Jet 2: 200t = d
323t + 200t = 2371
523t = 2371
t = approx 4.5 hours

Caleb and Ryan are basically the same as Alexis and Thomas

Answer 5

1) Let x = time you are looking for

Thomas will drive at 30 kph for x hours or

30x

Alexis will drive at 20 kph for x hours + the 3 hours she left before Thomas or

20(x+3)

Set the equations = to each other:

30x = 20(x+3)
30x = 20x + 60
10x = 60
x = 6 hours

Question 2 and 4 are done exactly the same.

3) 323x + 200x = 2371

You can do the rest

Answer 6

20(k+3)=30k ; k=?
20k + 60 = 30k
k=6 hours

47(k+2) = 58k
58k-47k=94
11k=94
k=8,55

323 k + 200k = 2371
523 k = 2371
k= 2371/523 = 4,53 hours

15(k+3) = 20k
15k + 45 =20k
45=5k; k=9 hours

Btw, this way you can't learn mathematics... But success on life does not necessarily depend on it. Thats the way you do business in real life. You always find someone who knows better but be prepared because it won't be for free... Thats why you need to be good at something. It may not be math but you sure need to be good at something so people will pay you... But after all who am I talking to :) you are still young, you will learn it by yourself.

Answer 7

alex and thomas:
The place where they meet is the place they both went the same distance. distance = speed * time.

20x = 30 (x - 3)
20x = 30x - 90
10x = 90
x = 9 hours
lets check:
alex 20 mph * 12 hrs = 240 miles (alex drives 3 hrs more than thomas, or 12 hours)
thomas 30 mph * 9 hrs = 240 miles

I will let you do the rest. I don't need the practice anymore.

Answer 8

1st question (explained):

their distances must equal
(20kph)(t) + (3hr)(20) = (30kph)(t)

t = 6 hrs

2nd question: t = 8.55 hrs

3rd question (explained):

Think of it as one plain staying still and the other traveling at (323 + 200), or 523. The distance traveled is 2371 @ 523 mph.
t = 4.53 hrs

4th question: t = 9 hrs

Answer 9

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Answer 10

6 hours
8.5 hours
4.55 hours
9 hours