Avi drove from his home to college 60 miles per hour. Returning over the same route, there was a lot of traffic, and he was only able to drive at 40 miles per hour. If the return trip took one hour longer, how many miles did he drive each way.
d = v t
60 t = 40 (t+1)
20 t = 40
t = 2
so
d = 60*2 = 120 miles
or
d = 40*3 = 120 miles
d=vt.
Let's assume the distance from Avi's home to college is "d" miles.
On the outbound trip, Avi drove at a speed of 60 miles per hour, so the time taken for Avi to travel from home to college is d/60 hours.
On the return trip, Avi drove at a speed of 40 miles per hour, and it took 1 hour longer, so the time taken for Avi to travel from college to home is d/40 hours + 1 hour.
Since the total time for the return trip is 1 hour longer than the outbound trip:
d/60 = d/40 + 1
To solve this equation, we need to get rid of the denominators:
Multiplying the entire equation by 120 (the least common multiple of 60 and 40) to eliminate the fractions, we get:
2d = 3d + 120
Subtracting 3d from both sides, we get:
2d - 3d = 120
Simplifying this equation, we get:
-d = 120
Dividing by -1, we get:
d = -120
Since distance cannot be negative, we made an error in solving the equation.
Let's change our assumption:
Assume the distance from Avi's home to college is "x" miles.
On the outbound trip, Avi drove at a speed of 60 miles per hour, so the time taken for Avi to travel from home to college is x/60 hours.
On the return trip, Avi drove at a speed of 40 miles per hour, and it took 1 hour longer, so the time taken for Avi to travel from college to home is x/40 hours + 1 hour.
Since the total time for the return trip is 1 hour longer than the outbound trip:
x/60 = x/40 + 1
To solve this equation, we need to get rid of the denominators:
Multiplying the entire equation by 120 (the least common multiple of 60 and 40) to eliminate the fractions, we get:
2x = 3x + 120
Subtracting 3x from both sides, we get:
2x - 3x = 120
Simplifying this equation, we get:
-x = 120
Dividing by -1, we get:
x = -120
Again, distance cannot be negative, which means we made the same mistake again.
Let's change our assumption one more time:
Assume the distance from Avi's home to college is "d" miles.
On the outbound trip, Avi drove at a speed of 60 miles per hour, so the time taken for Avi to travel from home to college is d/60 hours.
On the return trip, Avi drove at a speed of 40 miles per hour, and it took 1 hour longer, so the time taken for Avi to travel from college to home is d/40 hours + 1 hour.
Since the total time for the return trip is 1 hour longer than the outbound trip:
d/60 + 1 = d/40 ---------------(1)
Multiplying both sides of equation (1) by 120 (the least common multiple of 60 and 40), we get:
2d + 120 = 3d
Subtracting 2d from both sides, we get:
2d - 2d + 120 = 3d - 2d
120 = d
Therefore, Avi drove 120 miles each way.
To solve this problem, let's break it down step by step:
Let's assume the distance from Avi's home to college is 'd' miles.
Step 1: Calculate the time taken for Avi to drive from home to college.
Distance = Rate * Time
Time = Distance / Rate
Time taken to drive from home to college = d miles / 60 mph = d/60 hours
Step 2: Calculate the time taken for Avi to drive back from college to home.
Time taken to drive back = d miles / 40 mph = d/40 hours
Step 3: Find the difference in time taken for the return trip.
Difference in time taken = Time taken to drive back - Time taken to drive from home
(d/40) - (d/60) = 1 hour
Step 4: Solve the equation to find the value of 'd'.
Multiply the equation by 120 to eliminate the denominators:
3d - 2d = 120 (d/40) - 120 (d/60)
d = 120 miles
Therefore, Avi drove 120 miles each way (from home to college and back).