Solution:

Let the distance between Peter's (hereafter referred as P) and Rhea's (hereafter referred as R) be D.
When P and R meet for the first time, P has traveled 500 miles.
In that case, R has traveled (D - 500) miles.
=> Speed of P / Speed of R = 500 / (D - 500) ...... (1)

When P and R meet for the second time, P has traveled (D - 500) + 300 miles
Now, R has traveled (500 + D - 300)
=> Speed of P / Speed of R = 5 / (D - 5) ..... (2)

Equating (1) and (2)
500 / (D - 500) = (D - 2) / (D + 2)
D = 1200 Miles.

Solution:

3.75 hours

Explanation:
While you can solve it as you like, a simple mathematical equation can be used to find out.
Let M be the amount of petrol initially.
Let N be the time for which they drove.
According to the question, the amount of petrol used by first car in N hours = MN / 4
The amount of petrol used by second car in N hours = MN / 5
Hence, the amount of petrol left in the first car = (M - MN / 4)
The amount of petrol left in the second car = (M - MN / 5)
AS per the details given in the question, we can form the below equation:
M - MN / 5 = 4(M - MN / 4)
N = 15 / 4 or 3.75 hours.
Hence, both the drivers have driven the car for 3.75 hours at that particular time.

Solution:

36/71.

Explanation:

Solution:

The original price is $83.33.
(20 percent of the taxes are added to the selling price.)

Solution:

Joey sold 15 ice creams that day.

The fourth kid bought a single ice cream. Therefore, we have the following equation:
Total - (Total / 2 + 1/2) = 1
Solving it, we get the total as 3.

Let's work this method till we reach the first kid.

The first kid bought 15 / 2 + 1/2 = 8 (leaving 7)
The second kid bought 7 / 2 + 1/2 = 4 (leaving 3)
The third kid bought 3 / 2 + 1/2 = 2 (leaving 1)
The fourth kid bought 1 / 2 + 1/2 = 1

Adding all of them together, we get
8 + 4 + 2 + 1 = 15.

Solution:

80

Explanation:
21 B 7 C 9 D 10 A 13
= 21 / 7 + 9 X 10 - 13
= 3 + 90 - 13
= 80

Solution:

The total number of students is 500.

To follow how and why, please see the venn diagram.

Solution:

2nd

When the cylinder is spun for the first and last time, the following six outcomes are possible:

First:
First chamber is fired first. The first player loses.

Second:
Second chamber is fired first. The first player loses.

Third:
Third chamber is fired first. The first player loses.

Fourth:
Fourth chamber is fired first. The second player loses. (First shot, player 1, chamber 4 empty. Second shot player 2, chamber 5, empty. Third shot player 1, chamber 6 empty. Fourth shot player 2, chamber 1 not empty.)

Fifth:
Fifth chamber is fired first. The first player loses. (First shot, player 1, chamber 5 empty. Second shot player 2, chamber 6, empty. Third shot player 1, chamber 1 not empty.)

Sixth:
Sixth chamber is fired first. The second player loses. (First shot, player 1, chamber 6 empty. Second shot, player 2, chamber 1, not empty)

Thus, if you analyze, you will find that the second player has a 4/6 chance of winning. Therefore if you want to win the game, going second gives you better shot at it.

Solution:

75km

Explanation:
Distance between Bill and Darren = 40 km
Distance between Bill and Chris + Distance between Chris and Darren = 40 km
Distance between Bill and Chris + (Distance between Bill and Chris - 10) = 40 km
2 * Distance between Bill and Chris = 50 km
Distance between Bill and Chris = 25
Distance between Chris and Darren = 15 km

Therefore, distance between Darren's house and Alex's house = 60 + 15 = 75 km.

Solution:

She had a 50p coin, a 25p coin and four 10p coins.