I need to set up this problem algebraically. Also I can't figure out to work it out. It's a relative rate problem.
Bob leaves Bismarck traveling east along Interstate 94 at 65 mph. At the same time Tony leaves Fargo traveling west on Interstate 94. Since he is pulling a trailer, he can go only 45 mph. Fargo is 193 east of Bismarck. How long will it be until they meet?
let the time passes since they both left be t hours
Bob went 65t
Tony went 45t
but when they met the sum of their distances has to be 193
so 65t + 45t = 193
etc.
38g+46mg+4.2kg
To set up this problem algebraically, we can start by defining the variables and writing equations to represent the given information.
Let:
- The time it takes for Bob to reach the meeting point be represented by t (in hours).
- The time it takes for Tony to reach the meeting point be represented by t as well (since they meet at the same time).
- The distance Bob travels be represented by 65t (since his speed is 65 mph and time is t).
- The distance Tony travels be represented by 45t (since his speed is 45 mph and time is also t).
Now, let's write the equation for the problem. Since Bob and Tony are traveling towards each other, the sum of the distances they travel must be equal to the total distance between Bismarck and Fargo (which is 193 miles):
65t + 45t = 193
To solve this equation, we can combine like terms:
110t = 193
Finally, divide both sides of the equation by 110 to solve for t:
t = 193 / 110
Now, we can calculate the value of t to find out how long it will take for Bob and Tony to meet.