When Amy drives her car to work, the trip takes 1/2 hour. When she rides the bus, it takes 3/4 hour. The average speed of the bus is 12 mph less than her speed driving. Find the distance she travels to work.
See your 3:13 pm post for solution.
To find the distance Amy travels to work, we need to determine her driving speed and the bus's speed.
Let's assume that Amy's driving speed is x mph.
According to the given information, when Amy drives her car, the trip takes 1/2 hour. Therefore, we can use the formula: speed = distance / time.
Amy's driving speed is x mph and her time is 1/2 hour. Hence, the distance she travels when driving is:
Distance = Speed * Time
Distance = (x mph) * (1/2 hour)
Distance = (x/2) miles
Now, let's determine the bus's speed. We are given that the bus takes 3/4 hour to travel the same distance. We also know that the bus's speed is 12 mph less than Amy's driving speed.
So, the bus's speed can be calculated as (x mph - 12 mph).
Again, using the formula speed = distance / time, we know that:
Bus's speed = (Distance traveled while driving) / (Time taken by the bus)
Bus's speed = (x/2) miles / (3/4) hour
Bus's speed = (x/2) miles * (4/3) hour
Bus's speed = 2x/3 mph
Since we now have the bus's speed, we can set up an equation to find x:
x mph = (2x/3 mph) + 12 mph
To solve for x, multiply the equation by 3 to eliminate the fraction:
3x mph = 2x mph + 36 mph
Now, subtract 2x from both sides:
x mph = 36 mph
Therefore, Amy's driving speed is 36 mph.
Finally, we can find the distance Amy travels by substituting x = 36 mph into the formula we derived earlier:
Distance = (x/2) miles
Distance = (36 mph / 2) * (1/2 hour)
Distance = 18 miles
Therefore, Amy travels a distance of 18 miles to work.