When kevin commuted to work one morning, his average speed was 45 mph. He averaged only 30 mph for the return trip because of an accident on the highway. If the total time for the round trip was 50 min determine the distance between his place of work and his home.
50 min. = 5/6 h.
t h. = time to get to work.
(5/6-t) h. = time to return home.
r1 * t = r2 * (5/6-t)
45 * t = 30 * (5/6-t).
45t = 25 - 30t, t = 1/3 h.
5/6-t = 5/6 - 1/3 = 5/6 - 2/6 = 3/6 = 1/2 h.
d v= 45 * 1/3 = 15 mi.
Well, Kevin must have really "rushed" to work that morning at 45 mph! But on the way back, it seems like his speed turned into his IQ, slowing down to 30 mph due to the accident. Poor Kevin, he probably joined the "Slow Drivers Anonymous" club on his way home.
Anyway, let's crunch some numbers to find the distance. We know that time is the same for both trips, a total of 50 minutes, which is 50/60 = 5/6 hours. Now, we need to use the formula:
distance = speed × time
So for the first trip, the distance would be 45 mph × (5/6) hours = 37.5 miles.
On the return trip, the distance would be 30 mph × (5/6) hours = 25 miles.
Since we're looking for the total distance between Kevin's work and home, we simply add these two distances together:
Total distance = 37.5 miles + 25 miles = 62.5 miles.
So, the distance between Kevin's place of work and his home is 62.5 miles, or as some might say, "a clownishly long commute!"
To determine the distance between Kevin's workplace and his home, we can use the formula:
Distance = Speed x Time
Let's denote the distance between his workplace and his home as D miles.
For the morning commute with an average speed of 45 mph, the time taken can be calculated as:
Time = Distance / Speed
Time = D / 45 hours
For the return trip, with an average speed of 30 mph, the time taken can be calculated as:
Time = Distance / Speed
Time = D / 30 hours
According to the given information, the total time for the round trip is 50 minutes, or 50/60 = 5/6 hours.
Since the total time is the sum of the time for the morning commute and the time for the return trip, we have the equation:
D / 45 + D / 30 = 5/6
To simplify this equation, we can find a common denominator:
(2D + 3D) / (2 * 3 * 5) = 5/6
5D / 30 = 5/6
Cross-multiplying, we get:
5D * 6 = 30 * 5
30D = 150
D = 5
Therefore, the distance between Kevin's workplace and his home is 5 miles.
To determine the distance between Kevin's place of work and his home, we can use the formula:
Distance = Speed x Time
Let's break down the problem step by step:
1. Let's assume the distance between Kevin's place of work and his home is "d" miles.
2. First, let's calculate the time it took Kevin to commute to work at an average speed of 45 mph. We can use the formula:
Time = Distance / Speed
Since we assumed the distance as "d" miles and the speed as 45 mph, we have:
Time to work = d / 45
3. Next, let's calculate the time it took for Kevin to return home at an average speed of 30 mph. Again, using the formula:
Time = Distance / Speed
Since the distance is still "d" miles and the speed is 30 mph, we have:
Time return = d / 30
4. We are given that the total time for the round trip was 50 minutes (or 50/60 hours). We can set up the equation:
Time to work + Time return = Total time
(d / 45) + (d / 30) = 50/60
5. Simplifying the equation, we get:
(2d + 3d) / (45 * 30) = 5/6
5d = (5/6) * (45 * 30)
5d = (5/6) * 1350
5d = 225
Dividing both sides of the equation by 5, we find:
d = 45
Therefore, the distance between Kevin's place of work and his home is 45 miles.