Problem Solving

223. Car A is 20 miles behind car B which is tralling in the same direction along the same route as car A. Car A is travelling at a constant speed of 58 miles per hour and car B is travelling at a constant speed of 50 miles per hour. How many hours will it take for car A to overtake and drive 8 miles ahead of car B?
A. 1.5
B. 2.0
C. 2.5
D. 3.0
E. 3.5
OA E

234. In a crtain game, a large container is filled with red, yellow, green and blue beads worth respectively, 7,5,3 & 2 points each. A number of beads are then removed from the containr. If the product of the point values of the removed beads is 147,000, how many red beads were removed?
A. 5
B. 4
C. 3
D. 2
E. 0
OA D

Please help me with these problems. Thanks

223. Car A speed - Car B speed = 58-50 = 8 miles per hour

which means that Car A will have to cover 20 + 8 miles with an added
speed of 8 MPH
Thus, Time = 28 / 8 =3.5 hours

223. Car A is 20 miles behind car B which is tralling in the same direction along the same route as car A. Car A is travelling at a constant speed of 58 miles per hour and car B is travelling at a constant speed of 50 miles per hour. How many hours will it take for car A to overtake and drive 8 miles ahead of car B?

Car A 58/hr
Car B 50/hr

Car A is 20 miles behind and needs to catch up PLUS pass Car B by 8 miles.

So that means we can set up the following formula:

Let x = hours

58x = 50x + 28
8x = 28
x = 3.5


234. In a crtain game, a large container is filled with red, yellow, green and blue beads worth respectively, 7,5,3 & 2 points each. A number of beads are then removed from the containr. If the product of the point values of the removed beads is 147,000, how many red beads were removed?

Since the points are all prime factors and it is asking for the product you need to find all the prime factors of 147,000.

7 * 7 * 5 * 5 * 5 * 3 * 2 * 2 * 2

So the answer would be 2 red beads need to be removed.

234.
1000=10*10*10
147,000/1000=147

147=7*7*3

answer is D.

For the beads question, how do you know all the colors of the beads were removed? What if I only took out just red beads or any other color for that matter?