On a business trip a salesman traveled 40 mph for the first third of his trip and 50 mph for the remainder. If the entire trip took 4 hours and 20 minutes, how many miles did he travel?
any help is grately appreciated!
To solve this problem, you can use the formula: Distance = Speed * Time.
Let's break down the information given:
1. The salesman traveled 40 mph for the first third of his trip.
2. The salesman traveled 50 mph for the remainder of his trip.
3. The entire trip took 4 hours and 20 minutes.
First, convert 4 hours and 20 minutes to hours. Since there are 60 minutes in an hour, 20 minutes is equal to 20/60 = 1/3 of an hour. Therefore, the total time in hours is 4 + 1/3 = 13/3 hours.
Now, let's calculate the distance traveled in each portion of the trip.
For the first third of the trip, the salesman traveled at 40 mph for a certain amount of time. Let's call this time "t" hours. So, the distance traveled in this portion is 40 * t miles.
For the remaining portion of the trip, the salesman traveled at 50 mph for the remaining time, which is (13/3 - t) hours. So, the distance traveled in this portion is 50 * (13/3 - t) miles.
Since the entire trip distance is equal to the sum of these two distances, we can set up an equation:
40t + 50 * (13/3 - t) = Total distance
Now, we can solve this equation to find the value of "t":
40t + (50 * 13/3) - 50t = Total distance
40t - 50t + 650/3 = Total distance
-10t + 650/3 = Total distance
Now, we know that the entire trip took 4 hours and 20 minutes, which is equal to 13/3 hours. So, we can substitute this value into the equation:
-10 * (13/3) + 650/3 = Total distance
-130/3 + 650/3 = Total distance
520/3 = Total distance
Total distance = 173.33 miles (rounded to two decimal places).
Therefore, the salesman traveled approximately 173.33 miles on his business trip.