Mrs. Lewis plans to drive 900 miles to her vacation destination, driving an average 50 miles per hour. How many miles per hour faster must she average, while driving, to reduce her total driving time by 3 hours?
I'm not sure how to set up the equation. Thanks.
distance = rate x time
900 = 50*time
time = 900/50 = 18 hours.
To reduce the time by 3 hours means Mrs. Lewis must drive the 900 miles in 15 hours. Use the above to calculate the rate for 15 hours.
thx rose
15
To solve this problem, we can set up an equation based on the given information and solve for the unknown variable.
Let's assume that Mrs. Lewis drives x miles per hour faster to reduce her total driving time by 3 hours.
The total driving time can be calculated by dividing the total distance by the average speed. In this case, the total distance is 900 miles, and the average speed is 50 miles per hour.
So, the original driving time is given by:
Original driving time = Total distance / Average speed
= 900 miles / 50 miles per hour
Now, if Mrs. Lewis drives x miles per hour faster, her new average speed will be (50 + x) miles per hour.
To find the new driving time, we divide the total distance by the new average speed:
New driving time = Total distance / New average speed
= 900 miles / (50 + x) miles per hour
According to the problem statement, the new driving time is 3 hours less than the original driving time. So we can set up the equation:
Original driving time - New driving time = 3 hours
(900 miles / 50 miles per hour) - (900 miles / (50 + x) miles per hour) = 3 hours
Now we can solve this equation to find the value of x, which represents the number of miles per hour faster Mrs. Lewis must average:
(900 / 50) - (900 / (50 + x)) = 3
To solve this equation, we can simplify it by multiplying all terms by 50(50 + x) to eliminate the fractions:
(900)(50 + x) - (900)(50) = 3(50)(50 + x)
Now, we can solve for x by simplifying and solving the resulting linear equation.
Let's simplify the equation using the distributive property:
45,000 + 900x - 45,000 = 7,500 + 150x
Now, we can further simplify by combining like terms:
900x - 150x = 7,500
Simplifying the left side of the equation:
750x = 7,500
Dividing both sides by 750:
x = 7,500 / 750
Finally, dividing and simplifying:
x = 10
Therefore, Mrs. Lewis must drive 10 miles per hour faster to reduce her total driving time by 3 hours.