hi! can anyone help me with these 3 math problems??

Question

1.
2 cars leave the same place at the same time, but drive in opposite directions along a straight road. 1 car averages 55mi/h and the other 65mi/h. in how many hours will they be 250 miles apart?
a. about 1.7 hours
b. about 2.1 hours
c. about 3.8 hours
d. about 4.5 hours

2.
helen rode her bike for 2 hours at a constant speed of 6km/h. she took the same route to come home but increased her speed by 6km/h. how far did she ride?
a. 36km
b. 24km
c. 18km
d. 4.5km

3. A helicopter leaves an airport and flies south 180mi/h. 30 minutes later, an airplane leaves the airport and follows the same route as the helicopter, only at a higher elevation. the airplane is flying 330mi/h. how many minutes will it take the airplane to catch up to the helicopter?
a. 12
b. 24
c. 40
d. 48

ps: this is not my homework but a review for a midterm coming up. if u could explain how u got the answers it be great. thanks

Answer 1

55+65=120 so each hour they drive they get 120 miles apart.
so after 2 hrs the are 240 miles apart. So for 1 it is answer B.

for #2 it does not matter how much faster she went on the way home. If she was going 6km/hr for two hrs she traveled 12 km. Then it was 12 km home. So 12 +12 =24.

for #3 after 30 min the helicopter is 90 miles from the airport. dividing 180mi/60 min means the helicopter goes 3 miles per minute.

dividing 330mi/60 min means the plane goes 5.5 miles per minute. So after 40 mins the helicopter has gone 40*3=120 miles plus the 90 miles it was ahead for a total of 210 miles.

the plane after 40 minutes has gone 5.5*40=220 miles

Therefore c is the closest to the right answer

hope this is helpful

Answer 2

1. Suppose the point they start at is X. Car A is going to the left at 55 mph, and Car B is going to the right at 65 mph.

The distance Car A covers is 55T, where T is the time he travels. Car B covers 65T miles during the same time. At any point in time they are 55T + 65T miles apart (since they are going in opposite directions). This makes sense, since in 1 hour Car A will be 55 miles to the left, Car B is 65 miles to the right, making them 120 miles apart.

All we need to know is what is the value of T when the distance is 250 miles. That means:

55T + 65T = 250
120T = 250
T = 2.08333...

So b is the answer that's closest.

2. She rode 2 hours at 6 km/h which is 12 km. Since she took the same route home, she travelled 24 km total, and her speed coming home is irrelevent. That only affects WHEN she gets home, but that wasn't the question.

3. The location of the airplane at a point in time is 330T, where T is the number of hours. The helicopter took off a half hour before, so at the same time T the helicopter is at 180(T + .5). They meet when these two distances are equal:

180(T + .5) = 330T
180T + 90 = 330T
90 = 150T
T = .6 hours, or 36 minutes

I believe this is correct but it's not one of the choices. Are the numbers in the question right?

Answer 3

1.
Answers is b
t = time takes to get separation of 250 mi (in hours)
x1 = distance travelled by 55 mi/h car = 55 mi/h * t
x2 = distance travelled by 65 mi/h car = 65 mi/h * t

Now, x1+ x2 = 250
then, 55 * t + 65* t = 250
t = 2.08 ~ 2.1 hours

2 b
The physical distance does not change when sped up. Just that her time was shorter. So the total distance is twice the distance travelled when she was riding at 6 km/6

therefore, 2* 6km/h * 2 hours = 12 km

3 c
if t=0 is when the second plane starts,

and x = position of first plane
y = position of second plane
t= time in hours

x = speed of first plane * t + 90 = 180 * t + 90 (since first plane is 90 mi ahead of second plane when second plane starts)

y = 330 *t

now, you want t when x = y

180 t + 90 = 330t
t = 0.6 hours = 36 minutes so c

Answer 4

1) in one hour they have traveled a combined distance of 120 miles. This is how far apart they are. In 2 hours they have traveled 240 miles apart so the answer would be B

2) she rode an average speed of 9km/hr. If she rode for 2 hours she rode 18 km or C

I don't know 3 but you should be able to figure it out.

Answer 5

one is B like the guy said

2 = B
just assume shes going in a straight line, 2 hours at 6km/h puts her 12 km away, she took the same route home so she had to come home 12km

so 24 km

for number 3, im getting 36 minutes

Answer 6

All of your answers are B. Since you're given answer choices, just do trial and error. But simply put, with all these mph or kmph problems, just simply multiply by hours, be it 1 hours, .5 hour etc. So you'd still have to do trial and error to get to your answers. For instance, question 1: (55mph*2)+(65*2) = 110 + 130 = 240, you know your answer is little more than 2. Voila' there's your answer. For the second one, It took her 2 hours at 6kmph = 12km all together. She doubled her speed so you know it took her 12km to get to point A, she double her speed to 12kmph to get back home, and what do you get a total distance of 24km. And the third one, After 30 mins the helicopter went 90mi so for the plane to catch up: (24/60)*330=132mi. He actually will catch up and pass the helicopter.

Answer 7

B is the first answer, cause in 1 hour the first car would have driven 55 miles and the other 65 so that's a total of 120 miles so in two hours they would have driven 240 miles!

Answer 8

r*t =d
55t + 65t = 250
120t = 250
t = 2 1/12 hours = about 2.1 hours

d = r*t = 6*2 = 12km
So total distance = 2*12 = 24 km

330t = 180(t+30)
330t = 180t + 5400
150t = 5400
t = 5400/150 = 36 minutes
None of your answers is correct