Steve is driving to a ski resort. At first, he drove at a rate of 65 mph. Then a snow storm started and he had to slow down to 40 mph. In total. it took him 6 hours to drive 310 miles. Which system of equations represents this situation?
A. 6x + y= 1
x + y= 310
B. x + y= 105
6x + 40y=310
C. 310x + 65y= 40
x + y= 65
D. x + y=6
65x + 40y=310
The correct answer is D. x + y = 6 and 65x + 40y = 310.
Let's break down the given information step by step:
1. Steve drove at a rate of 65 mph initially.
Let's assign the variable x to represent the number of hours Steve drove initially at 65 mph.
2. Then, a snowstorm started, and he had to slow down to 40 mph.
Let's assign the variable y to represent the number of hours Steve drove at 40 mph after the snowstorm.
3. It took Steve a total of 6 hours to drive 310 miles.
The total time Steve drove is the sum of x and y, which can be represented as x + y = 6.
4. The total distance Steve drove is 310 miles.
The distance Steve drove at 65 mph is 65x, and the distance he drove at 40 mph is 40y. Therefore, the equation for the total distance can be represented as 65x + 40y = 310.
Combining these equations, we have the system of equations:
x + y = 6 (equation 1)
65x + 40y = 310 (equation 2)
Therefore, the correct answer is D. x + y = 6 and 65x + 40y = 310.
To find the correct system of equations that represent this situation, we need to analyze the given information:
1. Steve drove at a rate of 65 mph at first.
2. Then, he had to slow down to 40 mph due to a snow storm.
3. It took Steve 6 hours to drive a total distance of 310 miles.
Let's assign variables to the unknowns:
- Let x represent the number of hours Steve drove at 65 mph.
- Let y represent the number of hours Steve drove at 40 mph.
Now, let's break down the information into equations:
1. The distance travelled at the rate of 65 mph can be calculated as 65x.
2. The distance travelled at the rate of 40 mph can be calculated as 40y.
3. The total distance of 310 miles is the sum of the distances travelled at both speeds: 65x + 40y.
4. The total time taken to drive this distance is 6 hours, so the equation for total time is x + y = 6.
Based on this analysis, the correct system of equations representing this situation is:
x + y = 6,
65x + 40y = 310.
Therefore, the correct option is D. x + y = 6, 65x + 40y = 310.