Mary drove from Amity to Belleville at a speed of 50 mi/h. On the way back, she drove at 60 mi/h. The total trip took 4(2/5)h of driving time. Find the distance between there two cities
Let the distance each way be d
time for 1st trip = d/50
time for 2nd trip = d/60
d/50 + d/60 = 4.4
times 300
6d + 5d = 1320
11d = 1320
d = 120
distance between towns is 120 mi
To find the distance between the two cities, we can use the formula: distance = speed × time.
Let's start by calculating the time it took for Mary to drive from Amity to Belleville and back.
On the way from Amity to Belleville, Mary drove at a speed of 50 mi/h. Let's assume this took t1 hours.
On the way back from Belleville to Amity, Mary drove at a speed of 60 mi/h. Let's assume this took t2 hours.
According to the given information, the total trip took 4(2/5) hours of driving time. We can express this as a fraction: 4(2/5) = 22/5 hours.
Therefore, we have the equation: t1 + t2 = 22/5.
Now, we need to set up another equation to relate the distances. Since the distance between two cities is the same regardless of the direction, we can say that the distance from Amity to Belleville is equal to the distance from Belleville to Amity.
Let d be the distance between the two cities.
Distance from Amity to Belleville = Speed × Time = 50 mi/h × t1 = 50t1
Distance from Belleville to Amity = Speed × Time = 60 mi/h × t2 = 60t2
Since the distance is the same in both directions, we have the equation: 50t1 = 60t2.
Now, we have a system of two equations:
t1 + t2 = 22/5
50t1 = 60t2
We can solve this system of equations to find the values of t1 and t2.
First, we can solve the second equation for t1: t1 = 60t2/50
Simplifying, t1 = 6t2/5
Substituting t1 in the first equation:
6t2/5 + t2 = 22/5
Combining like terms:
(6t2 + 5t2)/5 = 22/5
Simplifying:
11t2/5 = 22/5
Cross-multiplying:
11t2 = 22
Solving for t2:
t2 = 22/11
Substituting the value of t2 back into the equation for t1:
t1 = 6t2/5
t1 = 6(22/11)/5
t1 = 12/5
Now we have the values of t1 and t2: t1 = 12/5 and t2 = 22/11.
To find the distance between the two cities, we can use the equation: distance = speed × time.
Using the value of t1 and speed of 50 mi/h:
Distance = 50 mi/h × (12/5) h
Distance = 600/5
Distance = 120 miles
Therefore, the distance between Amity and Belleville is 120 miles.
To find the distance between the two cities, we can use the formula: distance = speed × time.
Let's first find the time it took for Mary to drive from Amity to Belleville. Mary drove at a speed of 50 mi/h, and the time it took is unknown, so let's denote it as "t" hours.
Therefore, the distance from Amity to Belleville is 50 × t = 50t miles.
Now, let's find the time it took for Mary to drive back from Belleville to Amity. Mary drove at a speed of 60 mi/h, and the time it took is also unknown, so let's denote it as "t" hours.
Therefore, the distance from Belleville to Amity is 60 × t = 60t miles.
According to the given information, the total driving time is 4(2/5) hours. So, the sum of the times from both legs of the round trip is 4(2/5) hours.
t + t = 4(2/5)
2t = 4(2/5)
2t = 8/5
t = 4/5 hours
Now we can use either distance calculation (50t or 60t) to find the distance between the two cities. Let's use 50t, as it was mentioned first.
Distance = 50 × t
Distance = 50 × (4/5)
Distance = 200/5
Distance = 40 miles
Therefore, the distance between Amity and Belleville is 40 miles.