1. A car travels 20 kilometers per hour faster than a second car. The first car covers 180 kilometers in the same time the second covers 135 kilometers. What is the average speed of each car?
2. The tens' digit of a two-digit number is one more than its units' digit. If the number is divided by the sum of the digits, the quotient. What is the number?
1. F-20=S
180=F*t and 135=S*t or 180=F*135/S or
S=135/180 F put that into the first equation.
2. Makes no sense to me.
speed of 2nd car -- x
speed of 1st car -- x+20
time for 2nd car to go 135 km = 135/x
time for 1st car to go 180 km = 180/(x+20)
but aren't these two the same ?
Continue ....
In the second question, it looks like you did not finish the part where it tells us what the quotient is.
let unit's digit be x
then tens digit is x+1
then the number is 10(x+1) + x = 11x + 10
so (11x+10)/(x+(x+1)) = the quotient
continue
so whats the answer?
1. To find the average speed of each car, we need to first calculate the time it takes for each car to cover their respective distances. Let's assume the speed of the second car is x kilometers per hour.
The first car's speed is 20 kilometers per hour faster than the second car. Therefore, the speed of the first car is (x + 20) kilometers per hour.
Now, we can use the formula:
Time = Distance / Speed
For the first car, the time it takes to cover 180 kilometers is:
Time1 = 180 / (x + 20)
For the second car, the time it takes to cover 135 kilometers is:
Time2 = 135 / x
Since both cars travel for the same amount of time, we can set up an equation:
Time1 = Time2
180 / (x + 20) = 135 / x
To solve this equation, cross-multiply:
180x = 135(x + 20)
Now, distribute the 135:
180x = 135x + 2700
Simplify the equation:
45x = 2700
Divide both sides by 45:
x = 60
Now, we have the value of x, which is the speed of the second car.
The average speed of the first car is x + 20:
Speed of first car = 60 + 20 = 80 kilometers per hour
The average speed of the second car is x:
Speed of second car = 60 kilometers per hour
Therefore, the average speed of the first car is 80 kilometers per hour, and the average speed of the second car is 60 kilometers per hour.
2. Let's assume the tens' digit of the two-digit number is represented by T and the units' digit is represented by U.
According to the given condition, the tens' digit is one more than the units' digit:
T = U + 1
The number itself can be expressed as 10T + U.
We know that when the number is divided by the sum of its digits, the quotient is:
(10T + U) / (T + U)
We need to determine the number itself. To find it, we can substitute the value of T from the first equation into the second equation:
(10(U + 1) + U) / ((U + 1) + U)
Simplify inside the parentheses:
(10U + 10 + U) / (2U + 1)
Combine like terms:
(11U + 10) / (2U + 1)
Since this is a two-digit number, we have U as a single digit. We can test values of U to find when the quotient is also a whole number.
Starting with U = 1, let's substitute it into the equation:
(11(1) + 10) / (2(1) + 1) = 21 / 3 = 7
The quotient is a whole number, so the units' digit of the number is 1.
Therefore, the number can be written as 10T + U = 10(T) + 1 = 10T + 1
To find the exact value of T, let's test values of T:
If T = 1, the number would be 10(1) + 1 = 11, but this does not satisfy the condition that the tens' digit is one more than the units' digit.
If T = 2, the number would be 10(2) + 1 = 21, which satisfies the condition and matches the quotient we found earlier.
Therefore, the two-digit number is 21.