A bus leaves a station at 1 p.m, travling at an average rate of 44 mi/h. One hour later a second bus leaves the same station, travling east at a rate of 48 mi/h. At what time will the two buses be 274mi. apart?
Set up two equations as I did in the two previous problems. Let us know what you think and someone will be glad to help you through it.The secret to doing these word problems is to get the two equations. You need practice doing that. One think I saw the other day was a tutor said, "Write out the equation is English, then convert it to a math equatin." That works very well. Try it.
To solve this problem, we can set up two equations to represent the distances traveled by each bus.
Let's assume t represents the time in hours since the second bus left the station.
For the first bus, which traveled at an average rate of 44 mi/h, the distance traveled can be calculated by multiplying the time (t + 1) by the rate:
Distance_1 = 44(t + 1)
For the second bus, which traveled at a rate of 48 mi/h, the distance can be calculated by multiplying the time t by the rate:
Distance_2 = 48t
Since we want to find the time at which the two buses are 274 miles apart, we can set up the following equation:
Distance_1 - Distance_2 = 274
Substituting the expressions for Distance_1 and Distance_2 into the equation, we get:
44(t + 1) - 48t = 274
Now, we can solve this equation to find the value of t, which will represent the number of hours since the second bus left the station.
Expanding the equation, we have:
44t + 44 - 48t = 274
Combining like terms:
-4t + 44 = 274
Next, isolate the variable -4t by subtracting 44 from both sides of the equation:
-4t = 274 - 44
-4t = 230
To solve for t, divide both sides of the equation by -4:
t = 230 / -4
t = -57.5
Since time cannot be negative in this context, we can disregard the negative value.
Therefore, the two buses will be 274 miles apart after approximately 57.5 hours since the second bus left the station.
To determine the time when the two buses will be 274 miles apart, we need to add the time t to the time the second bus left the station. The second bus left one hour after the first bus, so the total time elapsed would be t + 1 hour.
Adding the time elapsed to 1 p.m. when the first bus left the station, we can determine the time when the two buses will be 274 miles apart.
Let's assume the first bus left the station at 1 p.m., then we can calculate the time as follows:
1 p.m. + t + 1 hour = 1 p.m. + 57.5 hours + 1 hour = 58.5 hours after 1 p.m.
Therefore, the two buses will be 274 miles apart at approximately 2:30 a.m. the following day.