Mary drove from Amity to Belleville at a speed of 50 mph. On the way back, she drove at 60 mph. The total trip took 4 2/5 hours of driving time. Find the distance between these two cities.
Any help would be greatly appreciated! =]
55 * (4.4)/2) = ? miles
To find the distance between Amity and Belleville, we can use the formula:
distance = speed × time
Let's calculate the time it took for Mary to drive from Amity to Belleville and back.
Let's assume the distance between the two cities is "d" miles.
When Mary drove from Amity to Belleville, she drove at a speed of 50 mph. Let's calculate the time it took for this leg of the trip.
time = distance / speed
= d / 50
On the way back, Mary drove at a speed of 60 mph. Again, let's calculate the time it took for this leg of the trip.
time = distance / speed
= d / 60
The total trip took 4 2/5 hours of driving time.
total time = time from Amity to Belleville + time from Belleville to Amity
= d / 50 + d / 60
We know that the total time is 4 2/5 hours. Let's convert it to a mixed fraction.
4 2/5 = (4 * 5 + 2) / 5 = 22 / 5
Now we can set up an equation:
22 / 5 = d / 50 + d / 60
To solve this equation, we need to find a common denominator for the two terms on the right-hand side. The common denominator is 300.
Rewriting the equation with the common denominator:
22 / 5 = (6d + 5d) / 300
Combining like terms:
22 / 5 = 11d / 300
To eliminate the fraction on both sides of the equation, we can cross-multiply.
(22)(300) = (5)(11d)
6600 = 55d
Divide both sides by 55:
d = 120
Therefore, the distance between Amity and Belleville is 120 miles.