I don't have any idea how to solve this. Could someone show me the steps in solving this word problem? I am at a loss!
Abus leaves a station at 1 pm., traveling west at a rate of 44 mi/h. One hour later a second bus leaves the same station, traveling east at a rate of 48 mi/h.What time will both of the buses be at 274 mi apart?
274= 44*time + 48(time-1)
solve for time.
I still can't firgure out how to answer this problem even though you provided the way. Could you give me the snswer and then show me how you got it?
Sure! To solve the problem, we will start by setting up an equation based on the given information. Let's assume that the time it takes for both buses to be 274 miles apart is "t" hours.
The first bus leaves at 1 pm and travels west at a rate of 44 mi/h. So, its distance traveled is 44t.
The second bus leaves one hour later (at 2 pm) and travels east at a rate of 48 mi/h. Since it left an hour later, its time traveled would be t - 1. And its distance traveled is 48(t - 1).
Now, we can set up the equation using the distances traveled by both buses:
44t + 48(t - 1) = 274
To solve for time (t), we can simplify the equation:
44t + 48t - 48 = 274
Combining like terms:
92t - 48 = 274
Next, we can isolate the variable by moving the constant term to the other side:
92t = 274 + 48
92t = 322
Finally, we can solve for t by dividing both sides of the equation by 92:
t = 322/92
By dividing, we get:
t = 3.5
Therefore, both buses will be 274 miles apart after 3.5 hours.
To summarize the steps:
1. Set up an equation based on the given information, using variables for the unknowns.
2. Simplify the equation.
3. Isolate the variable by moving constants to the other side.
4. Solve for the unknown variable.
5. Interpret the result in the context of the problem.
Please note that in this case, the time is measured in hours (since the rates are given in miles per hour), so the answer is 3.5 hours.