Bob drove 120 miles on his vacation. He drove an average of 1.2 times faster on the second 60 miles of his trip than he did on the first 60 miles of his trip. Which expression represents the time he spent driving? Let x = his speed on the first half of the trip.
The time he spent driving is equal to the sum of the time he spent driving on the first 60 miles and the time he spent driving on the second 60 miles:
Time = Time on first 60 miles + Time on second 60 miles
To find the time on each segment, we can use the formula:
Time = Distance / Speed
Time on first 60 miles = 60 / x
Time on second 60 miles = 60 / (1.2x) = 50 / x
The expression for the total time is:
Time = 60/x + 50/x = (110/x) hours
Note that the distance on the second 60 miles is only 50 miles since Bob drove 1.2 times faster, meaning he covered the distance in less time.
please select your answers from one of these choices.
A. 110 over x
B. 120 over x
C. 132 times x
D. 132 over x
A. 110 over x
Simplify. start fraction x over 7 x plus x squared end fraction
A. Start Fraction 1 over 7 plus lower x End Fraction semicolon where lower x does not equal negative 7
B. Start Fraction 1 over 7 lower x End Fraction semicolon where lower x does not equal zero
C. Start Fraction 1 over 7 plus lower x End Fraction semicolon where lower x does not equal zero comma negative 7
D. start fraction 1 over 7 end fraction
A. Start Fraction 1 over 7 plus lower x End Fraction; where lower x does not equal negative 7
Let's assume that Bob's speed on the first 60 miles of his trip is x miles per hour.
Since he drove 1.2 times faster on the second 60 miles, his speed on the second half of the trip would be 1.2x miles per hour.
To find the time he spent driving, we can use the formula: Time = Distance/Speed.
For the first 60 miles, the time spent driving would be: Time1 = 60 / x
For the second 60 miles, the time spent driving would be: Time2 = 60 / (1.2x)
The total time spent driving is the sum of the time spent on the first and second halves of the trip:
Total Time = Time1 + Time2 = 60 / x + 60 / (1.2x)
So, the expression that represents the time Bob spent driving is 60 / x + 60 / (1.2x).
To determine the time Bob spent driving, we need to divide the distance by his average speed.
Let's determine his speed on the second half of the trip first, which is 1.2 times faster than his speed on the first half.
His speed on the second 60 miles of the trip can be expressed as 1.2x, where x represents his speed on the first half of the trip.
Now, let's calculate the time it took Bob to drive the first 60 miles:
Time for the first half = Distance / Speed = 60 / x
Similarly, let's calculate the time it took Bob to drive the second 60 miles:
Time for the second half = Distance / Speed = 60 / (1.2x)
The total time spent driving is the sum of the times for the first and second halves:
Time = Time for the first half + Time for the second half
= 60 / x + 60 / (1.2x)
Therefore, the expression that represents the time Bob spent driving is:
Time = 60 / x + 60 / (1.2x)