Question

Two cars A and B are 200km apart and they are traveling toward each other at the speeds of 28km/h and 22 km/h respectively. When and where will they meet?

2.

If the car A and B in problem 1 start from the same point, going toward the same direction, at what time will they be 18km apart?


3.

If B starts at 1:00pm and gives chase starting at 1:15 from the same point as B, when and where will A overtake B?




Thank you so much for answering!!

Answer 1

like i was saying before distance traveled by car A + distance traveled by car B = total distance. do you agree?

Answer 2

yes

Answer 3

so what will be the total distance in this case?

Answer 4

d= 50kph?

Answer 5

kph means kilometers per hour. this is a unit of measurement for speed

Answer 6

oh.. right
it should be 50km?

Answer 7

is there a given 50 km in the problem?

Answer 8

no

Answer 9

which one is given in km?

Answer 10

is it 200km

Answer 11

yes that's the total distance

so distance traveled by car A + distance traveled by car B = 200

Answer 12

so now we need to find the distance traveled by car A and B

it is given that car A is traveling at 28 km/h

we know that distance = speed x time

let t = time

so distance traveled by car A is 28t

Answer 13

can you now find the distance traveled by car B?

Answer 14

ok

Answer 15

hint their time is the same

Answer 16

so the distance of Car B = 22t?

Answer 17

yup

Answer 18

so now add

28t + 22t = 200

solve for t

Answer 19

\[28t +22t = 200\]
\[50t \div50 = 200 \div 50\]
\[t = 4\]

Answer 20

right so time is 4 hours

Answer 21

they'll meet after 4 hours

Answer 22

as for where they'll meet i dont quite get what it wants

Answer 23

why not?
how should it be?

Answer 24

i dont know. like i said i dont know what it wants

Answer 25

an obvious answer is they'll meet at 0 km lol

Answer 26

ok

then, let's proceed

Answer 27

part 2 is exactly the same

Answer 28

ok, but is it done

Answer 29

how?

Answer 30

what's done?

Answer 31

* ok, but how is it done

how to do part 2?

Answer 32

same way distance traveled by car A + distance traveledby car B = total distance

Answer 33

\[28t + 22t = 18km\]
???

is that how i should start it?

Answer 34

yup

Answer 35

uhmm wait...

Answer 36

how do i get the Distance of A?

okkk

Answer 37

sorry should be subtraction..because its difference in speed

Answer 38

28t - 22t = 18

Answer 39

ok

Answer 40

so t= 3hrs?

Answer 41

yup

Answer 42

then. what's next?

Answer 43

for #3 it is unclear to me...can you rewrite it

Answer 44

Right.. sorry bout that.
If B starts at 1:00pm and A gives chase starting at 1:15 from the same point as B, when and where will A overtake B?

Answer 45

so if car b starts at 1 pm then let his time be t

car a starts at 1:15 so its time is t+15

agree?

Answer 46

uhmm sorry should be time of car A should be t-15 because it starts 15 minutes later than car B

Answer 47

ok

Answer 48

so when car A overtakes car B then their distance traveled will be the same agree>

Answer 49

yup

Answer 50

so do you have an idea what the equation will look like?

Answer 51

so should it be

t= t - 15

??

Answer 52

nope..that would just cancel out the t

Answer 53

remember

distance traveled by car A = distance traveled by car B

Answer 54

22t = 28t - 15

??

Answer 55

close

Answer 56

remember t - 15 is the time itself..

should be

22t = 28(t-15)

Answer 57

it makes a significant difference

Answer 58

oh.. ok

Answer 59

then we solve for t:

??

Answer 60

yes

Answer 61

22t = 28t - 420

420 = 28t - 22t

420 = 6t
--- ---
6 6

t = 70hrs

???

Answer 62

seems right

Answer 63

so A will overtake be after 70 hrs

??

Answer 64

where will A overtake B??/

Answer 65

just substitute

28(70-15)

Answer 66

ok

so D = 1,540 km

Answer 67

is D = 1,540 km

???

Answer 68

Yes u r right ..@alynamarie D= 1540 km

Answer 69

@mathslover thanks